Entanglement and excited-state quantum phase transition in an extended Dicke model

We investigate the properties of entanglement and excited-state quantum phase transition (ESQPT) in a hybrid atom-optomechanical system in which an optomechanical quadratic interaction is introduced into a normal Dicke model. Interestingly, by preparing the ancillary mode in a coherent state, both the quantum entanglement and ESQPT can be realized in a relative weak-coupling condition. Moreover, the entanglement is immune to the A² term, and a reversed trend of the entropy is obtained when the A² term is included. Density of states (DoS) and Peres lattice are used to investigate ESQPTs. Compared to a normal Dicke model, the DoS enlarges exp(2r_α) times if the ancillary mode is prepared in a coherent state. This work is an extension of the ground-state quantum phase transition, which may inspire further exploration of the quantum criticality in many-body systems.     

Global quantum discord and quantum phase transition in XY model

We study the relationship between the behavior of global quantum correlations and quantum phase transitions in XY model. We find that the two kinds of phase transitions in the studied model can be characterized by the features of global quantum discord (GQD) and the corresponding quantum correlations. We demonstrate that the maximum of the sum of all the nearest neighbor bipartite GQDs is effective and accurate for signaling the Ising quantum phase transition, in contrast, the sudden change of GQD is very suitable for characterizing another phase transition in the XY model. This may shed lights on the study of properties of quantum correlations in different quantum phases.     

具有三体相互作用的自旋链系统中的几何相位与量子相变

本文首先对具有三体相互作用的一维自旋链系统的哈密顿量进行了对角化．然后通过一个旋转操作求解了系统基态的几何相位,通过数值计算几何相位及其导数随外界参数的变化,考虑三体相互作用对几何相位以及量子相变的影响,结果表明几何相位可以很好的用来表征该系统中的量子相变,并且发现三体相互作用不但引起相变点平移,而且可以产生新的临界点．     

Genuine tripartite entanglement and quantum phase transition

A new simplified formula is presented to characterize genuine tripartite entanglement of （2 2 n）-dimensional quantum pure states. The formula turns out equivalent to that given in （Quant. Inf. Comp. 7（7） 584 （2007））, hence it also shows that the genuine tripartite entanglement can be described only on the basis of the local （2 2）-dimensional reduced density matrix. In particular, the two exactly solvable models of spin system studied by Yang （Phys. Rev. A 71 030302（R） （2005）） are reconsidered by employing the formula. The results show that a discontinuity in the first derivative of the formula or in the formula itself of the ground state just corresponds to the existence of quantum phase transition, which is obviously different from the concurrence.     

Photonic phase transition in circuit quantum electrodynamics lattices coupled to superconducting phase qubits

A hybrid quantum architecture was proposed to engineer a localization-delocalization phase transition of light in a two-dimension square lattices of superconducting coplanar waveguide resonators, which are interconnected by current-biased Josephson junction phase qubits. We find that the competition between the on-site repulsion and the nonlocal photonic hopping leads to the Mott insulator-superfluid transition. By using the mean-field approach and the quantum master equation, the phase boundary between these two different phases could be obtained when the dissipative effects of superconducting resonators and phase qubit are considered. The good tunability of the effective on-site repulsion and photon-hopping strengths enable quantum simulation on condensed matter physics and many-body models using such a superconducting resonator lattice system. The experimental feasibility is discussed using the currently available technology in the circuit QED.     

The deconfining phase transition in lattice quantum chromodynamics

We present a large-scale Monte Carlo calculation of the deconfining phase transition temperature in lattice quantum chromodynamics without fermions. Using the Wilson action, the transition temperature as a function of the lattice couplingg is consistent with scaling behavior dictated by the perturbativeα function for 6/g²>6.15. Speaker at the conference; on leave from CRIP, Budapest.     

Rényi entropy and quantum phase transition in the Dicke model

The Rényi entropies of the Dicke model are presented. This quantum-optical model describes a single-mode bosonic field interacting with an ensemble of N two-level atoms. There is a quantum phase transition in the N→∞ limit. It is shown that there is an abrupt change in the Rényi entropy of order β at the transition point. Around the critical value of the coupling strength λc the Rényi entropy is proportional to the logarithm of the characteristic length and diverges as ln|λc−λ| for any order β. The pseudocapacity defined here in analogy with the heat capacity exhibits the phase transition. The critical exponent for the Dicke model is found to be 1 for any value of the parameter β.     

Optically induced phase transition of excitons in coupled quantum dots

The weak classical light excitations in many semiconductor quantum dots have been chosen as important solid- state quantum systems for processing quantum information and implementing quantum computing. For strong classical light we predict theoretically a novel phase transition as a function of magnitude of this classical light from the deformed to the normal phases in resonance ease, and the essential features of criticality such as the scaling behaviour, critical exponent and universality are also present in this paper.     

Dynamics of a quantum phase transition and relaxation to a steady state

We review recent theoretical work on two closely related issues: excitation of an isolated quantum condensed matter system driven adiabatically across a continuous quantum phase transition or a gapless phase, and apparent relaxation of an excited system after a sudden quench of a parameter in its Hamiltonian. Accordingly, the review is divided into two parts. The first part revolves around a quantum version of the Kibble–Zurek mechanism including also phenomena that go beyond this simple paradigm. What they have in common is that excitation of a gapless many-body system scales with a power of the driving rate. The second part attempts a systematic presentation of recent results and conjectures on apparent relaxation of a pure state of an isolated quantum many-body system after its excitation by a sudden quench. This research is motivated in part by recent experimental developments in the physics of ultracold atoms with potential applications in the adiabatic quantum state preparation and quantum computation.     

Discord under the influence of a quantum phase transition

This paper studies the discord of a bipartite two-level system coupling to an XY spin-chain environment in a transverse field and investigates the relationship between the discord property and the environment’s quantum phase transition.The results show that the quantum discord is also able to characterize the quantum phase transitions.We also discuss the difference between discord and entanglement,and show that quantum discord may reveal more general information than quantum entanglement for characterizing the environment’s quantum phase transition.     

Dynamical quantum phase transition in XY chains with the Dzyaloshinskii-Moriya and XZY-YZX three-site interactions

We study the dynamical quantum phase transitions (DQPTs) in the $XY$ chains with the Dzyaloshinskii-Moriya interaction and the $XZY$-$YZX$ type of three-site interaction after a sudden quench. Both the models can be mapped to the spinless free fermion models by the Jordan-Wigner and Bogoliubov transformations with the form $H=\sum_{k}ǎrepsilon_{k}(\eta^{†}_{k}\eta_{k}-\frac{1}{2})$, where the quasiparticle excitation spectra $ǎrepsilon_{k}$ may be smaller than 0 for some $k$ and are asymmetrical ($ǎrepsilon_{k}\neqǎrepsilon_{-k}$). It is found that the factors of Loschmidt echo equal 1 for some $k$ corresponding to the quasiparticle excitation spectra of the pre-quench Hamiltonian satisfying $ǎrepsilon_{k}\cdotǎrepsilon_{-k}<0$, when the quench is from the gapless phase. By considering the quench from different ground states, we obtain the conditions for the occurrence of DQPTs for the general $XY$ chains with gapless phase, and find that the DQPTs may not occur in the quench across the quantum phase transitions regardless of whether the quench is from the gapless phase to gapped phase or from the gapped phase to gapless phase. This is different from the DQPTs in the case of quench from the gapped phase to gapped phase, in which the DQPTs will always appear. Moreover, we analyze the different reasons for the absence of DQPTs in the quench from the gapless phase and the gapped phase. The conclusion can also be extended to the general quantum spin chains.     

Quantum information entropy for one-dimensional system undergoing quantum phase transition

Calculations of the quantum information entropy have been extended to a non-analytically solvable situation. Specifically, we have investigated the information entropy for a one-dimensional system with a schematic "Landau" potential in a numerical way. Particularly, it is found that the phase transitional behavior of the system can be well expressed by the evolution of quantum information entropy. The calculated results also indicate that the position entropy S_x and the momentum entropy S_p at the critical point of phase transition may vary with the mass parameter M but their sum remains as a constant independent of M for a given excited state. In addition, the entropy uncertainty relation is proven to be robust during the whole process of the phase transition.     

Quantum coherence and ground-state phase transition in a four-chain Bose–Hubbard model

We study the quantum coherence and ground-state phase transition of a four-chain Bose–Hubbard model with the long-range interaction. In a special four-chain Bose–Hubbard model,i.e., each chain only has one optical potential, four types of the ground-state phases are discovered. The effects of the disorder, the on-site interaction and the long-range interaction on the quantum coherence are studied. For the system without the long-range interaction, the quantum coherence changes from one periodic oscillation to two periodic oscillations as the onsite interaction increases. By considering the long-range interaction, the quantum coherence goes back to one periodic oscillation again. The on-site interaction itself suppresses the quantum coherence, both the on-site interaction and long-range interaction together enhance the quantum coherence with the weak disorder. If the disorder strength is increased beyond a critical value,they start to suppress the quantum coherence. In a regular four-chain Bose–Hubbard model, i.e.,each chain has many optical potentials, the ground-state phase transitions are obtained by using the cluster Gutzwiller mean-field method. Exotic ground-state phases are found, i.e., superfluid phase, integer Mott insulator phase, supersolid phase and loophole insulator phase. The combination of the loophole insulator phase and the supersolid phase expands the lobes with the half-integer filling per site for the small ratio β = t_■/t_⊥.     

Universal order-parameter and quantum phase transition for two-dimensional q-state quantum Potts model

We investigate quantum phase transitions for q-state quantum Potts models (q=2,3,4) on a square lattice and for the Ising model on a honeycomb lattice by using the infinite projected entangled-pair state algorithm with a simplified updating scheme. We extend the universal order parameter to a two-dimensional lattice system, which allows us to explore quantum phase transitions with symmetry-broken order for any translation-invariant quantum lattice system of the symmetry group G. The universal order parameter is zero in the symmetric phase, and it ranges from zero to unity in the symmetry-broken phase. The ground-state fidelity per lattice site is computed, and a pinch point is identified on the fidelity surface near the critical point. The results offer another example highlighting the connection between (i) critical points for a quantum many-body system undergoing a quantum phase-transition and (ii) pinch points on a fidelity surface. In addition, we discuss three quantum coherence measures: the quantum Jensen-Shannon divergence, the relative entropy of coherence, and the l₁ norm of coherence, which are singular at the critical point, thereby identifying quantum phase transitions.     

Entanglement and quantum phase transition in the extended Hubbard model

We study quantum entanglement in a one-dimensional correlated fermionic system. Our results show, for the first time, that entanglement can be used to identify quantum phase transitions in fermionic systems.     

嵌套正方格子上反铁磁高斯模型的相变

采用等效变化的方法,把嵌套正方晶格转化为可求解的正方晶格。利用重整化群变换,我们求得了正方系统的临界点。结合本文中给出的两个变换关系,得到了嵌套正方晶格上反铁磁高斯模型的临界点为 K=-0.707b。     

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.     

嵌套正方格子上反铁磁高斯模型的相变

采用等效变换的方法,把嵌套正方晶格转化为可求解的正方晶格.利用重整化群变换,我们求得了正方系统的临界点.结合本文中给出的两个变换关系,得到了嵌套正方晶格上反铁磁高斯模型的临界点为K*=-0.707b.     

Possible phase transition of anisotropic frustrated Heisenberg model at finite temperature

The frustrated spin-1/2 J_1a–J_1b–J₂ antiferromagnet with anisotropy on the two-dimensional square lattice was investigated, where the parameters J_1aand J_1b represent the nearest neighbor exchanges and along the x and y directions, respectively. J₂ represents the next-nearest neighbor exchange. The anisotropy includes the spatial and exchange anisotropies. Using the double-time Green’s function method, the effects of the interplay of exchanges and anisotropy on the possible phase transition of the Néel state and stripe state were discussed. Our results indicated that, in the case of anisotropic parameter 0≤η<1, the Néel and stripe states can exist and have the same critical temperature as long as J₂ = J_1b/2. Under such parameters, a first-order phase transformation between the Néel and stripe states can occur below the critical point. For J₂ ≠J_1b/2, our results indicate that the Néel and stripe states can also exist, while their critical temperatures differ. When J₂>J_1b/2, a first-order phase transformation between the two states may also occur. However, for J₂<J_1b/2, the Néel state is always more stable than the stripe state.