Mottness is at the heart of the essential physics in a strongly correlated system as many novel quantum phenomena occur in the metallic phase near the Mott metal–insulator transition. We investigate the Mott transiti...Mottness is at the heart of the essential physics in a strongly correlated system as many novel quantum phenomena occur in the metallic phase near the Mott metal–insulator transition. We investigate the Mott transition in a Hubbard model by using the dynamical mean-field theory and introduce the local quantum state fidelity to depict the Mott metal–insulator transition. The local quantum state fidelity provides a convenient approach to determining the critical point of the Mott transition. Additionally, it presents a consistent description of the two distinct forms of the Mott transition points.展开更多
In this paper we deal with the existence of infinitely many critical points of the even functional I(u)=integral from n=Q to (F(x,u,Du))+integral from n=(?)Q to (G(x,u)), u∈W^(1,p)(Ω),where G(x, u)=integral from n=o...In this paper we deal with the existence of infinitely many critical points of the even functional I(u)=integral from n=Q to (F(x,u,Du))+integral from n=(?)Q to (G(x,u)), u∈W^(1,p)(Ω),where G(x, u)=integral from n=o to u (g(x,t)dt), under the weak structure conditions on F(x, u, q) by the Mountain Pass Lemma.展开更多
In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value ...In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value problems in [C. Bonanno and P. Candito, Appl. Anal., 88（4） （2009）, pp. 605-616], we construct two new strong maximum principles and obtain that the boundary value problem has three positive solutions for λ and μ in some suitable intervals. The approaches we use are the critical point theory.展开更多
In this paper, the existence and nonexistence of solutions to a class of quasilinear elliptic equations with nonsmooth functionals are discussed, and the results obtained are applied to quasilinear SchrSdinger equatio...In this paper, the existence and nonexistence of solutions to a class of quasilinear elliptic equations with nonsmooth functionals are discussed, and the results obtained are applied to quasilinear SchrSdinger equations with negative parameter which arose from the study of self-channeling of high-power ultrashort laser in matter.展开更多
In order to generalize Hadamard's theory of fundamental solutions to the case of degenerate holomorphic PDE, this paper studies the asymptotic expansion of Dirac-type distribution associated with a class of hypers...In order to generalize Hadamard's theory of fundamental solutions to the case of degenerate holomorphic PDE, this paper studies the asymptotic expansion of Dirac-type distribution associated with a class of hypersurfaces F(x) with degenerate critical points and proves that [F(x)](+)(lambda) is a distribution-valued meromorphic of lambda is an element of C under some assumptions on F(x). Next, the authors use the Normal form theory of Arnold and prove that for a hypersurface F(x) = 0 with A(mu) type degenerate critical point at x = 0, F-+(lambda) is a distribution-valued meromorphic function of lambda.展开更多
We study the critical scaling and dynamical signatures of fractionalized excitations at two different deconfined quantum critical points(DQCPs)in an S=1/2 spin chain using the time evolution of infinite matrix product...We study the critical scaling and dynamical signatures of fractionalized excitations at two different deconfined quantum critical points(DQCPs)in an S=1/2 spin chain using the time evolution of infinite matrix product states.The scaling of the correlation functions and the dispersion of the conserved current correlations explicitly show the emergence of enhanced continuous symmetries at these DQCPs.The dynamical structure factors in several different channels reveal the development of deconfined fractionalized excitations at the DQCPs.Furthermore,we find an effective spin-charge separation at the DQCP between the ferromagnetic(FM)and valence bond solid(VBS)phases,and identify two continua associated with different types of fractionalized excitations at the DQCP between the X-direction and Z-direction FM phases.Our findings not only provide direct evidence for the DQCP in one dimension but also shed light on exploring the DQCP in higher dimensions.展开更多
We present a new method to identify the critical point for the Bose-Einstein condensation （BEC） of a trapped Bose gas. We calculate the momentum distribution of an interacting Bose gas near the critical temperature,...We present a new method to identify the critical point for the Bose-Einstein condensation （BEC） of a trapped Bose gas. We calculate the momentum distribution of an interacting Bose gas near the critical temperature, and find that it deviates significantly from the Gaussian profile as the temperature approaches the critical point. More importantly, the standard deviation between the calculated momentum spectrum and the Gaussian profile at the same temperature shows a turning point at the critical point, which can be used to determine the critical temperature. These predictions are also confirmed by our BEC experiment for magnetically trapped ST Rb gases.展开更多
One could tune a topological double-Weyl semimetal or a topological triple-Weyl semimetal to become a topologically trivial insulator by opening a band gap.This kind of quantum phase transition is characterized by the...One could tune a topological double-Weyl semimetal or a topological triple-Weyl semimetal to become a topologically trivial insulator by opening a band gap.This kind of quantum phase transition is characterized by the change of certain topological invariant.A new gapless semimetallic state emerges at each topological quantum critical point.Here we perform a renormalization group analysis to investigate the stability of such critical points against perturbations induced by random scalar potential and random vector potential.We find that the quantum critical point between double-Weyl semimetal and band insulator is unstable and can be easily turned into a compressible diffusive metal by any type of weak disorder.The quantum critical point between triple-Weyl semimetal and band insulator flows to a stable strong-coupling fixed point if the system contains a random vector potential merely along the z-axis,but becomes a compressible diffusive metal when other types of disorders exist.展开更多
Deconfined quantum critical points(DQCPs)have been proposed as a class of continuous quantum phase transitions occurring between two ordered phases with distinct symmetry-breaking patterns,beyond the conventional fram...Deconfined quantum critical points(DQCPs)have been proposed as a class of continuous quantum phase transitions occurring between two ordered phases with distinct symmetry-breaking patterns,beyond the conventional framework of Landau-Ginzburg-Wilson(LGW)theory.At the DQCP,the system exhibits emergent gauge fields,fractionalized excitations,and enhanced symmetries.展开更多
We calculate the quark number susceptibility （QNS） around the chiral critical end point （CEP）. The CEP is found to be located at （μc,Tc）= （80 MeV, 148 MeV） where μc and Tc are the critical chemical potential...We calculate the quark number susceptibility （QNS） around the chiral critical end point （CEP）. The CEP is found to be located at （μc,Tc）= （80 MeV, 148 MeV） where μc and Tc are the critical chemical potential and temperature, respectively. The QNS is found to have the highest and sharpest peak at the CEP. It is also found that, when the chemical potential μ is in the range of 60MeV≤ μ ≤ 110MeV, the QNS near the transition temperature is larger than the free field result, which indicates that the space-like damping mode dominates the degree of freedom of motion near the CEP.展开更多
A coalescence model was employed to form deuterons(d),tritons(t),and helium-3(^(3)He)nuclei from a uniformly-distributed volume of protons(p)and neutrons(n).We studied the ratio N_(t)N_(p)/N_(d)^(2)of light nuclei yie...A coalescence model was employed to form deuterons(d),tritons(t),and helium-3(^(3)He)nuclei from a uniformly-distributed volume of protons(p)and neutrons(n).We studied the ratio N_(t)N_(p)/N_(d)^(2)of light nuclei yields as a function of the neutron density fluctuations.We investigated the effect of finite transverse momentum(p_(T))acceptance on the ratio,in particular,the“extrapolation factor”(f)for the ratio as a function of the p_(T)spectral shape and the magnitude of neutron density fluctuations.The nature of f was found to be monotonic in p_(T)spectra“temperature”parameter and neutron density fluctuation magnitude;variations in the latter are relatively small.We also examined f in realistic simulations using the kinematic distributions of protons measured from the heavy-ion collision data.The nature of f was found to be smooth and monotonic as a function of the beam energy.Therefore,we conclude that extrapolation from limited p_(T)ranges does not create,enhance,or reduce the local peak of the N_(t)N_(p)/N_(d)^(2)ratio in the beam energy.Our study provides a necessary benchmark for light nuclei ratios as a probe for nucleon density fluctuations,an important observation in the search for the critical point of nuclear matter.展开更多
In this paper, we consider the problem of existence as well as multiplicity results for a bi-harmonic equation under the Navier boundary conditions： △2 u = K（x）u p , u 〉 0 in Ω , △u = u = 0 on Ω , where Ω is ...In this paper, we consider the problem of existence as well as multiplicity results for a bi-harmonic equation under the Navier boundary conditions： △2 u = K（x）u p , u 〉 0 in Ω , △u = u = 0 on Ω , where Ω is a smooth domain in R n , n 5, and p ＋ 1 = 2 n n 4 is the critical Sobolev exponent. We obtain highlightly a new criterion of existence, which provides existence results for a dense subset of positive functions, and generalizes Bahri-Coron type criterion in dimension six. Our argument gives also estimates on the Morse index of the obtained solutions and extends some known results. Moreover, it provides, for generic K, Morse inequalities at infinity, which delivers lower bounds for the number of solutions. As further applications of this Morse theoretical approach, we prove more existence results.展开更多
In this article several existence theorems on multiple solutions for the twopoint boundary value problem with resonance at, both infinity and zero are proved.
This paper is concerned with the harmonic equation(P;) : ?u = 0, u > 0 in B;and ?u/?ν+(（n-2）/2)u =(（n-2）/2) Ku;on S;where B;is the unit ball in R;, n ≥ 4 with Euclidean metric g;, ?B;= S;is its boundary, K is...This paper is concerned with the harmonic equation(P;) : ?u = 0, u > 0 in B;and ?u/?ν+(（n-2）/2)u =(（n-2）/2) Ku;on S;where B;is the unit ball in R;, n ≥ 4 with Euclidean metric g;, ?B;= S;is its boundary, K is a function on S;and ε is a small positive parameter. We construct solutions of the subcritical equation(P;) which blow up at one critical point of K. We give also a sufficient condition on the function K to ensure the nonexistence of solutions for(P;) which blow up at one point. Finally, we prove a nonexistence result of single peaked solutions for the supercritical equation(P;).展开更多
This paper deals with the existence of solutions to the elliptic equation-△u-μ/|x|2=λu +|u|2*-2u + f(x,u) in Ω,u = 0 on (?)Ω, where Ω is a bounded domain in RN(N≥3), 0 ∈ Ω 2*=2N/N-2,λ> 0, λ (?) σμ,σμ...This paper deals with the existence of solutions to the elliptic equation-△u-μ/|x|2=λu +|u|2*-2u + f(x,u) in Ω,u = 0 on (?)Ω, where Ω is a bounded domain in RN(N≥3), 0 ∈ Ω 2*=2N/N-2,λ> 0, λ (?) σμ,σμ is the spectrum of the operator -△-μI/|x|2 with zero Dirichlet boundary condition, 0 <μ< μ-,μ-=(N-2)2/4, f(x,u)is an asymmetric lower order perturbation of |u|2* -1 at infinity. Using the dual variational methods, the existence of nontrivial solutions is proved.展开更多
The quantum critical regime marks a zone in the phase diagram where quantum fluctuation around the critical point plays a significant role at finite temperatures.While it is of great physical interest,simulation of th...The quantum critical regime marks a zone in the phase diagram where quantum fluctuation around the critical point plays a significant role at finite temperatures.While it is of great physical interest,simulation of the quantum critical regime can be difficult on a classical computer due to its intrinsic complexity.Herein,we propose a variational approach,which minimizes the variational free energy,to simulate and locate the quantum critical regime on a quantum computer.The variational quantum algorithm adopts an ansatz by performing an unitary operator on a product of a single-qubit mixed state,in which the entropy can be analytically obtained from the initial state,and thus the free energy can be accessed conveniently.With numeral simulation,using the one-dimensional Kitaev model as a demonstration we show that the quantum critical regime can be identified by accurately evaluating the temperature crossover line.Moreover,the dependencies of both the correlation length and the phase coherence time with temperature are evaluated for the thermal states.Our work suggests a practical way as well as a first step for investigating quantum critical systems at finite temperatures on quantum devices with few qubits.展开更多
The measurements on temperature dependences of magnetic susceptibility χ（T）, specific heat C（T）, and electrical resistivity ρ（T） were carried out for the antiferromagnetic（AFM）（Ce（1-x）Lax）2Ir3Ge5（0 ≤ x...The measurements on temperature dependences of magnetic susceptibility χ（T）, specific heat C（T）, and electrical resistivity ρ（T） were carried out for the antiferromagnetic（AFM）（Ce（1-x）Lax）2Ir3Ge5（0 ≤ x ≤ 0.66） system. It was found that the Neel temperature TNdecreases with increasing La content x, and reaches 0 K near a critical content xcr =0.6. A new phase diagram was constructed based on these measurements. A non-Fermi liquid behavior in ρ（T） and a log T relationship in C（T） were found in the samples near xcr, indicating them to be near an AFM quantum critical point（QCP） with strong spin fluctuation. Our finding indicates that（Ce（1-x）Lax）2Ir3Ge5 may be a new platform to search for unconventional superconductivity.展开更多
In this paper, we give a Z 2 index theory of generalized critical point. By this theory we get a sufficient condition on the existing result of a class functional, as an example we give a new result that the equa...In this paper, we give a Z 2 index theory of generalized critical point. By this theory we get a sufficient condition on the existing result of a class functional, as an example we give a new result that the equation-Δu+u=｜u｜ p-1 u, x∈R N,(1)has infinite solutions.展开更多
In this paper, we study a class of p（x）-biharmonic equations with Navier boundary condition. Using the mountain pass theorem, fountain theorem, local linking theorem and symmetric mountain pass theorem, we establish...In this paper, we study a class of p（x）-biharmonic equations with Navier boundary condition. Using the mountain pass theorem, fountain theorem, local linking theorem and symmetric mountain pass theorem, we establish the existence of at least one solution and infinitely many solutions of this problem, respectively.展开更多
An existent theorem is obtained for nonzero W-1,W-2(R-N) solutions of the following equations on R-N -Delta u + b(x)u = f(x,u), x is an element of R-N, where b is periodic for some variables and coercive for the other...An existent theorem is obtained for nonzero W-1,W-2(R-N) solutions of the following equations on R-N -Delta u + b(x)u = f(x,u), x is an element of R-N, where b is periodic for some variables and coercive for the others, f is superlinear.展开更多
基金Project supported by the Scientific Research Foundation for Youth Academic Talent of Inner Mongolia University (Grant No.1000023112101/010)the Fundamental Research Funds for the Central Universities of China (Grant No.JN200208)+2 种基金supported by the National Natural Science Foundation of China (Grant No.11474023)supported by the National Key Research and Development Program of China (Grant No.2021YFA1401803)the National Natural Science Foundation of China (Grant Nos.11974051 and 11734002)。
文摘Mottness is at the heart of the essential physics in a strongly correlated system as many novel quantum phenomena occur in the metallic phase near the Mott metal–insulator transition. We investigate the Mott transition in a Hubbard model by using the dynamical mean-field theory and introduce the local quantum state fidelity to depict the Mott metal–insulator transition. The local quantum state fidelity provides a convenient approach to determining the critical point of the Mott transition. Additionally, it presents a consistent description of the two distinct forms of the Mott transition points.
文摘In this paper we deal with the existence of infinitely many critical points of the even functional I(u)=integral from n=Q to (F(x,u,Du))+integral from n=(?)Q to (G(x,u)), u∈W^(1,p)(Ω),where G(x, u)=integral from n=o to u (g(x,t)dt), under the weak structure conditions on F(x, u, q) by the Mountain Pass Lemma.
基金Supported by NSFC(11326127,11101335)NWNULKQN-11-23the Fundamental Research Funds for the Gansu Universities
文摘In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value problems in [C. Bonanno and P. Candito, Appl. Anal., 88（4） （2009）, pp. 605-616], we construct two new strong maximum principles and obtain that the boundary value problem has three positive solutions for λ and μ in some suitable intervals. The approaches we use are the critical point theory.
基金supported by NSF of China(11201488),supported by NSF of China(11371146)Hunan Provincial Natural Science Foundation of China(14JJ4002)
文摘In this paper, the existence and nonexistence of solutions to a class of quasilinear elliptic equations with nonsmooth functionals are discussed, and the results obtained are applied to quasilinear SchrSdinger equations with negative parameter which arose from the study of self-channeling of high-power ultrashort laser in matter.
文摘In order to generalize Hadamard's theory of fundamental solutions to the case of degenerate holomorphic PDE, this paper studies the asymptotic expansion of Dirac-type distribution associated with a class of hypersurfaces F(x) with degenerate critical points and proves that [F(x)](+)(lambda) is a distribution-valued meromorphic of lambda is an element of C under some assumptions on F(x). Next, the authors use the Normal form theory of Arnold and prove that for a hypersurface F(x) = 0 with A(mu) type degenerate critical point at x = 0, F-+(lambda) is a distribution-valued meromorphic function of lambda.
基金Project supported by the National Science Foundation of China(Grant No.12174441)the Fundamental Research Funds for the Central Universities,Chinathe Research Funds of Remnin University of China(Grant No.18XNLG24)。
文摘We study the critical scaling and dynamical signatures of fractionalized excitations at two different deconfined quantum critical points(DQCPs)in an S=1/2 spin chain using the time evolution of infinite matrix product states.The scaling of the correlation functions and the dispersion of the conserved current correlations explicitly show the emergence of enhanced continuous symmetries at these DQCPs.The dynamical structure factors in several different channels reveal the development of deconfined fractionalized excitations at the DQCPs.Furthermore,we find an effective spin-charge separation at the DQCP between the ferromagnetic(FM)and valence bond solid(VBS)phases,and identify two continua associated with different types of fractionalized excitations at the DQCP between the X-direction and Z-direction FM phases.Our findings not only provide direct evidence for the DQCP in one dimension but also shed light on exploring the DQCP in higher dimensions.
基金Supported by the National Natural Science Foundation of China under Grant No 11104322the National Key Basic Research and Development Program of China under Grant No 2011CB921503
文摘We present a new method to identify the critical point for the Bose-Einstein condensation （BEC） of a trapped Bose gas. We calculate the momentum distribution of an interacting Bose gas near the critical temperature, and find that it deviates significantly from the Gaussian profile as the temperature approaches the critical point. More importantly, the standard deviation between the calculated momentum spectrum and the Gaussian profile at the same temperature shows a turning point at the critical point, which can be used to determine the critical temperature. These predictions are also confirmed by our BEC experiment for magnetically trapped ST Rb gases.
基金the Natural Science Foundation of Anhui Province,China(Grant No.2208085MA11)the National Natural Science Foundation of China(Grants Nos.11974356,12274414,and U1832209)。
文摘One could tune a topological double-Weyl semimetal or a topological triple-Weyl semimetal to become a topologically trivial insulator by opening a band gap.This kind of quantum phase transition is characterized by the change of certain topological invariant.A new gapless semimetallic state emerges at each topological quantum critical point.Here we perform a renormalization group analysis to investigate the stability of such critical points against perturbations induced by random scalar potential and random vector potential.We find that the quantum critical point between double-Weyl semimetal and band insulator is unstable and can be easily turned into a compressible diffusive metal by any type of weak disorder.The quantum critical point between triple-Weyl semimetal and band insulator flows to a stable strong-coupling fixed point if the system contains a random vector potential merely along the z-axis,but becomes a compressible diffusive metal when other types of disorders exist.
基金supported by the National Natural Science Foundation of China(Grant Nos.12134020 and 12374156)the National Key Research and Development Program of China(Grant No.2023YFA1406500)。
文摘Deconfined quantum critical points(DQCPs)have been proposed as a class of continuous quantum phase transitions occurring between two ordered phases with distinct symmetry-breaking patterns,beyond the conventional framework of Landau-Ginzburg-Wilson(LGW)theory.At the DQCP,the system exhibits emergent gauge fields,fractionalized excitations,and enhanced symmetries.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11105122,11275097 and 11475085the Foundation of Graduate School of Nanjing University under Grant No 2014CL02
文摘We calculate the quark number susceptibility （QNS） around the chiral critical end point （CEP）. The CEP is found to be located at （μc,Tc）= （80 MeV, 148 MeV） where μc and Tc are the critical chemical potential and temperature, respectively. The QNS is found to have the highest and sharpest peak at the CEP. It is also found that, when the chemical potential μ is in the range of 60MeV≤ μ ≤ 110MeV, the QNS near the transition temperature is larger than the free field result, which indicates that the space-like damping mode dominates the degree of freedom of motion near the CEP.
基金supported in part by the U.S.Department of Energy(No.DE-SC0012910)National Nature Science Foundation of China(Nos.12035006 and 12075085)the Ministry of Science and Technology of China(No.2020YFE020200)。
文摘A coalescence model was employed to form deuterons(d),tritons(t),and helium-3(^(3)He)nuclei from a uniformly-distributed volume of protons(p)and neutrons(n).We studied the ratio N_(t)N_(p)/N_(d)^(2)of light nuclei yields as a function of the neutron density fluctuations.We investigated the effect of finite transverse momentum(p_(T))acceptance on the ratio,in particular,the“extrapolation factor”(f)for the ratio as a function of the p_(T)spectral shape and the magnitude of neutron density fluctuations.The nature of f was found to be monotonic in p_(T)spectra“temperature”parameter and neutron density fluctuation magnitude;variations in the latter are relatively small.We also examined f in realistic simulations using the kinematic distributions of protons measured from the heavy-ion collision data.The nature of f was found to be smooth and monotonic as a function of the beam energy.Therefore,we conclude that extrapolation from limited p_(T)ranges does not create,enhance,or reduce the local peak of the N_(t)N_(p)/N_(d)^(2)ratio in the beam energy.Our study provides a necessary benchmark for light nuclei ratios as a probe for nucleon density fluctuations,an important observation in the search for the critical point of nuclear matter.
文摘In this paper, we consider the problem of existence as well as multiplicity results for a bi-harmonic equation under the Navier boundary conditions： △2 u = K（x）u p , u 〉 0 in Ω , △u = u = 0 on Ω , where Ω is a smooth domain in R n , n 5, and p ＋ 1 = 2 n n 4 is the critical Sobolev exponent. We obtain highlightly a new criterion of existence, which provides existence results for a dense subset of positive functions, and generalizes Bahri-Coron type criterion in dimension six. Our argument gives also estimates on the Morse index of the obtained solutions and extends some known results. Moreover, it provides, for generic K, Morse inequalities at infinity, which delivers lower bounds for the number of solutions. As further applications of this Morse theoretical approach, we prove more existence results.
基金Supported by the Natural Science Foundation of China(10471098)the Beijing Natural Science Foundation(1052004)the Foundation of Beijing's Educational Committee(KM200510028001)the Key-Project of NSFB-FBEC
文摘In this article several existence theorems on multiple solutions for the twopoint boundary value problem with resonance at, both infinity and zero are proved.
基金the Deanship of Scientific Research at Taibah University on material and moral support in the financing of this research project
文摘This paper is concerned with the harmonic equation(P;) : ?u = 0, u > 0 in B;and ?u/?ν+(（n-2）/2)u =(（n-2）/2) Ku;on S;where B;is the unit ball in R;, n ≥ 4 with Euclidean metric g;, ?B;= S;is its boundary, K is a function on S;and ε is a small positive parameter. We construct solutions of the subcritical equation(P;) which blow up at one critical point of K. We give also a sufficient condition on the function K to ensure the nonexistence of solutions for(P;) which blow up at one point. Finally, we prove a nonexistence result of single peaked solutions for the supercritical equation(P;).
文摘This paper deals with the existence of solutions to the elliptic equation-△u-μ/|x|2=λu +|u|2*-2u + f(x,u) in Ω,u = 0 on (?)Ω, where Ω is a bounded domain in RN(N≥3), 0 ∈ Ω 2*=2N/N-2,λ> 0, λ (?) σμ,σμ is the spectrum of the operator -△-μI/|x|2 with zero Dirichlet boundary condition, 0 <μ< μ-,μ-=(N-2)2/4, f(x,u)is an asymmetric lower order perturbation of |u|2* -1 at infinity. Using the dual variational methods, the existence of nontrivial solutions is proved.
基金supported by the National Natural Science Foundation of China(Grant No.12005065)the Guangdong Basic and Applied Basic Research Fund(Grant No.2021A1515010317)。
文摘The quantum critical regime marks a zone in the phase diagram where quantum fluctuation around the critical point plays a significant role at finite temperatures.While it is of great physical interest,simulation of the quantum critical regime can be difficult on a classical computer due to its intrinsic complexity.Herein,we propose a variational approach,which minimizes the variational free energy,to simulate and locate the quantum critical regime on a quantum computer.The variational quantum algorithm adopts an ansatz by performing an unitary operator on a product of a single-qubit mixed state,in which the entropy can be analytically obtained from the initial state,and thus the free energy can be accessed conveniently.With numeral simulation,using the one-dimensional Kitaev model as a demonstration we show that the quantum critical regime can be identified by accurately evaluating the temperature crossover line.Moreover,the dependencies of both the correlation length and the phase coherence time with temperature are evaluated for the thermal states.Our work suggests a practical way as well as a first step for investigating quantum critical systems at finite temperatures on quantum devices with few qubits.
基金supported by the National Basic Research Program of China(Grant Nos.2016FYA0300402,2015CB921004,and 2012CB821404)the National Natural Science Foundation of China(Grant Nos.11374261 and 11204059)
文摘The measurements on temperature dependences of magnetic susceptibility χ（T）, specific heat C（T）, and electrical resistivity ρ（T） were carried out for the antiferromagnetic（AFM）（Ce（1-x）Lax）2Ir3Ge5（0 ≤ x ≤ 0.66） system. It was found that the Neel temperature TNdecreases with increasing La content x, and reaches 0 K near a critical content xcr =0.6. A new phase diagram was constructed based on these measurements. A non-Fermi liquid behavior in ρ（T） and a log T relationship in C（T） were found in the samples near xcr, indicating them to be near an AFM quantum critical point（QCP） with strong spin fluctuation. Our finding indicates that（Ce（1-x）Lax）2Ir3Ge5 may be a new platform to search for unconventional superconductivity.
文摘In this paper, we give a Z 2 index theory of generalized critical point. By this theory we get a sufficient condition on the existing result of a class functional, as an example we give a new result that the equation-Δu+u=｜u｜ p-1 u, x∈R N,(1)has infinite solutions.
基金supported by the National Natural Science Foundation of China(11071198)Scientific Research Fund of SUSE(2011KY03)Scientific Reserch Fund of Sichuan Provincial Education Department(12ZB081)
文摘In this paper, we study a class of p（x）-biharmonic equations with Navier boundary condition. Using the mountain pass theorem, fountain theorem, local linking theorem and symmetric mountain pass theorem, we establish the existence of at least one solution and infinitely many solutions of this problem, respectively.
文摘An existent theorem is obtained for nonzero W-1,W-2(R-N) solutions of the following equations on R-N -Delta u + b(x)u = f(x,u), x is an element of R-N, where b is periodic for some variables and coercive for the others, f is superlinear.
