一维扩展量子罗盘模型的拓扑序和量子相变

应用矩阵乘积态表示的无限虚时间演化块算法,研究了扩展的量子罗盘模型.为了深入研究该模型的长程拓扑序和量子相变,基于奇数键和偶数键,引入了奇数弦关联和偶数弦关联,计算了保真度、奇数弦关联、偶数弦关联、奇数弦关联饱和性与序参量.弦关联表现出三种截然不同的行为:衰减为零、单调饱和与振荡饱和.基于弦关联的以上特征,给出了量子罗盘模型的基态序参量相图.在临界区,局域磁化强度和单调奇弦序参量的临界指数β=1/8表明:相变的普适类是Ising类型.此外,保真度探测到的相变点、连续性与非连续性和序参量的结果一致.     

两腿XXZ自旋梯子模型的量子相变与量子临界现象

对于无限大尺寸两腿自旋1/2的XXZ自旋梯子模型,通过运用基于随机行走的张量网络(TN)算法数值模拟出基态波函数,首次尝试研究自旋梯子模型的约化保真度、普适序参量、纠缠熵等物理观测量,并系统研究基态保真度的三维挤点与二维分叉、约化保真度的分叉、局域序参量、普适序参量、纠缠熵和量子相变之间存在的关联关系.基于张量网络表示的算法在任意随机选择初始状态时,可以得到两腿XXZ量子自旋梯子系统简并的对称破缺基态波函数,该基态波函数是由于Z2对称破缺引起的.本文期望所提供的方法可为进一步研究凝聚态物质中热力学极限下的强关联电子量子晶格自旋梯子系统的量子相变和量子临界现象提供一种更有效的强大的工具.     

Geometrical approach to the thermodynamical theory of phase transitions of the second kind

A geometrical approach to the phenomenological theory of phase transitions of the second kind at constant pressure P and variable temperature T is proposed. Equilibrium states of a system at zero external field and fixed P and T are described by points in three-dimensional space with coordinates η, the order parameter, T, the temperature and /gf, the thermodynamic potential. These points form the so-called zero field curve in the (η, T, /gf) space. Its branch point coincides with the critical point of the system. The small parameter of the theory (the distance from the critical point along the zero-field curve) is shown to be more convenient than the small parameter of the Landau theory. It is emphasized that no explicit functional dependency of /gf on η and T is imposed.

It is shown that using (η, T, /gf) space one cannot overcome well-known difficulties of the Landau theory of phase transitions and describe non-analytical behavior of real systems in the vicinity of the critical point. This becomes possible only if one increases the dimensionality of the space, taking into account the dependency of the thermodynamic potential not only on η and T, but also on near (local) order parameters λ_i. In this case under certain conditions it is possible to describe anomalous increase of the specific heat when the temperature of the system approaches the critical point from above as well as from below the critical temperature T_c.     

二维３态Potts量子系统的保真度与序参量

二维无限正方格子上的量子3态Potts模型是发生一级相变还是二级相变?通过运用无限纠缠投影对态 (iPEPS) 算法,在进行数值模拟时任意选取初态,能得到二维无限正方格子上的3态Potts模型的三个不同的简并基态波函数,这些简并的情况是由自发对称性破缺引起的.首先,揭示了在二维系统中自发对称性破缺引起的相变可以运用单点基态保真度的分叉来研究,也反映了在二维系统中约化保真度同样有一个分叉行为;再者,还提出了二维系统的普适序参量以及多分量的复数局域序参量的行为来尝试研究二维3态Potts模型,共同确定系统发生的量子相变的临界点及其类型.即基于iPEPS算法,从单点基态保真度、约化保真度、普适序参量以及局域序参量的角度,来研究3态Potts模型的量子相变,其为一级相变.     

二维３态Potts量子系统的保真度与序参量

二维无限正方格子上的量子3态Potts模型是发生一级相变还是二级相变?通过运用无限纠缠投影对态算法(iPEPS),在进行数值模拟时任意选取初态,能得到二维无限正方格子上的3态Potts模型的三个不同的简并基态波函数,这些简并的情况是由自发对称性破缺引起的.首先,揭示了在二维系统中自发对称性破缺引起的相变可以运用单点基态保真度的分叉来研究,也反映了在二维系统中约化保真度同样有一个分叉行为;再者,还开创性提出了二维系统的普适序参量以及多分量的复数局域序参量的行为来尝试研究二维3态Potts模型,共同确定系统发生的量子相变的临界点及其类型.即基于iPEPS算法,从单点基态保真度、约化保真度、普适序参量以及局域序参量的角度,来研究3态Potts模型的量子相变,其为一级相变.     

二维3态Potts量子系统的保真度与序参量

二维无限正方格子上的量子3态Potts模型是发生一级相变还是二级相变?通过运用无限纠缠投影对态(i PEPS)算法,在进行数值模拟时任意选取初态,能得到二维无限正方格子上的3态Potts模型的三个不同的简并基态波函数,这些简并的情况是由自发对称性破缺引起的.首先,揭示了在二维系统中自发对称性破缺引起的相变可以运用单点基态保真度的分叉来研究,也反映了在二维系统中约化保真度同样有一个分叉行为;再者,还提出了二维系统的普适序参量以及多分量的复数局域序参量的行为来尝试研究二维3态Potts模型,共同确定系统发生的量子相变的临界点及其类型.即基于i PEPS算法,从单点基态保真度、约化保真度、普适序参量以及局域序参量的角度,来研究3态Potts模型的量子相变,其为一级相变.     

Fidelity spectrum: A tool to probe the property of a quantum phase

Fidelity measures the similarity between two states and is widely adapted by the condensed matter community as a probe of quantum phase transitions in many-body systems. Despite its success in witnessing quantum critical points,information about the fine structure of a quantum phase one can get from this approach is still limited. Here, we proposed a scheme called fidelity spectrum. By studying the fidelity spectrum, one can obtain information about the characteristics of a phase. In particular, we investigated the spectra in the one-dimensional transverse-field Ising model and the twodimensional Kitaev model on a honeycomb lattice. It was found that the spectra have qualitative differences in the critical and non-critical regions of the two models. From the distributions of them, the dominating k modes in a particular phase could also be captured.     

Critical Kondo destruction and the violation of the quantum-to-classical mapping of quantum criticality

Antiferromagnetic heavy fermion metals close to their quantum critical points display a richness in their physical properties unanticipated by the traditional approach to quantum criticality, which describes the critical properties solely in terms of fluctuations of the order parameter. This has led to the question as to how the Kondo effect gets destroyed as the system undergoes a phase change. In one approach to the problem, Kondo lattice systems are studied through a self-consistent Bose-Fermi Kondo model within the extended dynamical mean field theory. The quantum phase transition of the Kondo lattice is thus mapped onto that of a sub-Ohmic Bose-Fermi Kondo model. In the present article we address some aspects of the failure of the standard order-parameter functional for the Kondo-destroying quantum critical point of the Bose-Fermi Kondo model.     

Thermal Hall conductivity with sign change in the Heisenberg–Kitaev kagome magnet

The Heisenberg-Kitaev(HK) model on various lattices has attracted a lot of attention because it may lead to exotic states such as quantum spin liquid and topological orders.The rare-earth-based kagome lattice(KL) compounds Mg₂RE₃Sb₃O₁₄(RE=Gd,Er) and(RE=Nd) have q=0,120° order and canted ferromagnetic(CFM) order,respectively.Interestingly,the HK model on the KL has the same ground state long-range orders.In the theoretical phase diagram,the CFM phase re...     

One-way quantum deficit and quantum coherence in the anisotropic <Emphasis Type="Italic">XY</Emphasis> chain

In this study, we investigate pairwise non-classical correlations measured using a one-way quantum deficit as well as quantum coherence in the XY spin-1/2 chain in a transverse magnetic field for both zero and finite temperatures. The analytical and numerical results of our investigations are presented. In the case when the temperature is zero, it is shown that the one-way quantum deficit can characterize quantum phase transitions as well as quantum coherence. We find that these measures have a clear critical point at λ = 1. When λ ≤ 1, the one-way quantum deficit has an analytical expression that coincides with the relative entropy of coherence. We also study an XX model and an Ising chain at the finite temperatures.     

一维自旋1键交替XXZ链中的量子纠缠和临界指数

利用基于张量网络表示的矩阵乘积态算法以及无限虚时间演化块抽取方法,本文研究了一维无限格点自旋1的键交替反铁磁XXZ海森伯模型中的量子相变.分别计算了系统的von Neumann熵、单位格点保真度和序参量,从而得到了系统随键交替强度的变化从拓扑有序Néel相到局域有序二聚化相的量子相变点.我们用矩阵乘积态方法拟合出了相变的中心荷c?0.5,表明此相变属于二维经典的Ising普适类.另外,通过对拓扑Néel序的数值拟合,我们得到了相变点处的特征临界指数β′=0.236和γ′=0.838.     

Biorthogonal quantum criticality in non-Hermitian many-body systems

We develop the perturbation theory of the fidelity susceptibility in biorthogonal bases for arbitrary interacting non-Hermitian many-body systems with real eigenvalues. The quantum criticality in the non-Hermitian transverse field Ising chain is investigated by the second derivative of the ground-state energy and the ground-state fidelity susceptibility. We show that the system undergoes a second-order phase transition with the Ising universal class by numerically computing the critical points and the critical exponents from the finite-size scaling theory. Interestingly, our results indicate that the biorthogonal quantum phase transitions are described by the biorthogonal fidelity susceptibility instead of the conventional fidelity susceptibility.     

三维钻石型等级晶格上量子Heisenberg系统的临界性质

利用重整化群方法,研究了三维钻石型等级晶格上的各向异性量子Heisenberg模型,获得了系统的相图和临界性质. 结果表明:对于铁磁系统,在各向同性Heisenberg极限下,系统存在有限温度的相变,并计算了系统的序参量和临界指数; 对于反铁磁系统,在各向同性Heisenberg极限下,临界温度不等于零,在临界线上不存在重入行为.     

Site-diluted quantum Heisenberg spin model applied to the magnetic properties of Fe–Al disordered alloys

In this work we present a theoretical study of the magnetic behavior of disordered Fe–Al alloys on the basis of a simple-diluted quantum Heisenberg spin model with the assumption that the exchange interaction J depends on the Al concentration q. We calculated the critical temperature and exponents through the mean field renormalization group method. An acceptable fit to the experimental phase diagram for Al concentration in the range 0.30q0.45 is obtained.     

Detection of quantum critical points by a probe qubit

Quantum phase transitions occur when the ground state of a quantum system undergoes a qualitative change when an external control parameter reaches a critical value. Here, we demonstrate a technique for studying quantum systems undergoing a phase transition by coupling the system to a probe qubit. It uses directly the increased sensibility of the quantum system to perturbations when it is close to a critical point. Using an NMR quantum simulator, we demonstrate this measurement technique for two different types of quantum phase transitions in an Ising spin chain.     

Model of quantum criticality in He3 bilayers adsorbed on graphite

Recent experiments on He3 bilayers adsorbed on graphite have shown striking quantum critical properties at the point where the first layer localizes. We model this system with the Anderson lattice plus interlayer Coulomb repulsion in two dimensions. Assuming that quantum critical fluctuations come from a vanishing of the effective hybridization, we can reproduce several features of the system, including the apparent occurrence of two quantum critical points, the variation of the effective mass and coherence temperature with coverage.     

First and second order quantum phase transitions in multi-band superconductors

In multi-band and inter-metallic materials superconductivity can be destroyed by applying external pressure in these systems. In many cases the critical temperature is driven continuously to zero, the superconducting to normal transition being associated with a superconducting quantum critical point (SQCP). In this paper we propose a model for this type of SQCP based on the increase of hybridization as pressure is applied in the material. We study a two-band superconductor with hybridization V between these bands. We use a BCS approximation and include both inter- and intra-band attractive interactions. We show that for negligible inter-band interactions, as hybridization increases there is a second order phase transition from a superconductor to a normal state at zero temperature at a critical value of the hybridization V_c. This SQCP can be reached by pressure, since this external parameter controls hybridization in the system. We also find discontinuous transitions at zero temperature and the appearance of a gapless superconducting (GS) phase in a certain range of hybridization in the case of inter-band interactions being dominant.     

具有Dzyaloshinskii-Moriya相互作用的XY模型的量子相干性

研究了具有Dzyaloshinskii-Moriya(DM)相互作用的一维横场XY自旋链的量子相变和量子相干性.采用约旦-维格纳变换严格求解了哈密顿量,并描绘了体系的关联函数和相图,相图包含反铁磁相、顺磁相和螺旋相.利用相对熵和Jensen-Shannon熵讨论了XY模型的量子相干性.研究发现,相对熵与Jensen-Shannon熵所表现的行为都可以很好地表征该模型的量子相变.非螺旋相中量子相干性不依赖DM相互作用,而在螺旋相DM相互作用对量子相干性有显著影响.此外,指出了在带有DM相互作用的这一类反射对称破缺体系中关联函数计算的常见问题.     

Phase Diagram of the Spin-1/2 Heisenberg Alternating Chain in a Magnetic Field *

By using the infinite time-evolving block decimation, we study quantum fidelity and entanglemententropy in the spin-1/2 Heisenberg alternating chain under an external magnetic field .The effects of the magnetic field on the fidelity are investigated, and its relation with the quantum hase transition (QPT) is analyzed. The phase diagram of the model is given accordingly, which supports the Haldane phase, the singlet-dimer phase, the Luttinger liquid phase and the paramagnetic phase. The scaling of entanglement entropy in the gapless Luttinger liquid phase is studied, and the central charge $c=1$ is obtained. We also study the relationship between the quantum coherence, string order parameter and QPTs. Results obtained from these quantum information observations are consistent with the previous reports.     

Picturing quantum phase transitions

We discuss the quantum phase transitions (QPT) in N-spin chains from the point of view of collective observables. We show that the measurement space representation is a convenient tool for the analysis of phase transitions, allowing the determination of an appropriate set of macroscopic order parameters (for a given Hamiltonian). Quantum correlations in the vicinity of the critical points are analyzed both in the ground states and low temperature thermal states.