Functional Integrals and Variational-Cumulant Expansion in sine-Gordon-Thirring Model

The free energy in 1D sine-Gordon-Thirring model with impurity coupling is studied by means of functional integrals and variational-cumulant expansion methods. Two variational parameters are introduced to evaluate free energy and statistical averages. It is shown that the non-perturbation method of functional integrals can be applied to strong-coupling range of fermion systems.     

Functional Integrals and Variational-Cumulant Expansion in sine-Gordon-Thirring Model

The free energy in 1D sine-Gordon- Thirring model with impurity coupling is studied by means of functional integrals and variational-cumulant expansion methods. Two variational parameters are introduced to evaluate free energy and statistical averages. It is shown that the non-perturbation method of functional integrals can be applied to strongcoupling range of fcrmion systems.     

Quantum Spin Systems at Positive Temperature

We develop a novel approach to phase transitions in quantum spin models based on a relation to their classical counterparts. Explicitly, we show that whenever chessboard estimates can be used to prove a phase transition in the classical model, the corresponding quantum model will have a similar phase transition, provided the inverse temperature β and the magnitude of the quantum spins satisfy . From the quantum system we require that it is reflection positive and that it has a meaningful classical limit; the core technical estimate may be described as an extension of the Berezin-Lieb inequalities down to the level of matrix elements. The general theory is applied to prove phase transitions in various quantum spin systems with . The most notable examples are the quantum orbital-compass model on and the quantum 120-degree model on which are shown to exhibit symmetry breaking at low-temperatures despite the infinite degeneracy of their (classical) ground state.     

A Trial of Variational-Cumulant Expansion on Simple Ising Model With Second Order Phase Transition

The standard variational-cumulant expansion (VC) combined with a scheme for the enumeration of connected diagrams is employed to study the simple Ising model with the second-order phase transition. This model is evaluated to the 5th order approximations. A comparison with the 2-dimensional exact results shows that thermodynamic quantities converge rather slowly to the exact values in the intermediate region. A strict analytical calculation of the critical temperature with the 5th order approxinlation both for J_i and cumulant expansion suggests that VC chn achieve rather high standard accuracy if the variational parameters J_i could be determined up to higher degrees of corrections rather than the first one. Anomalies are found for U, C and M at extremely low temperature. A detailed study of M implies that thermodynamic formulae should be carefully chosen in VC approach so as to avoid these anomalies.     

Variational-Cumulant Expansion up to the Sixth Order Approximation on 2-Dimensional Ising Model

To study the variational-cumulant expansion (VCE) method, the 2-dimensional Ising model has been selected. The model is evaluated to the sixth order approximation with a scheme for the enumeration of connected diagrams. The internal energy (U), specific.heat (C) and spontaneous magnetization (M) have been calculated. A comparison with the exact results shows that thermodynamic and magnetic quantities converge to the exact values rather quickly and the position of phase transition point approaches to the exact pointstand order by order.     

The Critical Points of a Generalized Mixed Spin Model with Free Fermion Approximation

A generalized mixed spin model with anisotropic interactions is considered on the union jack lattice. We find that the model is equivalent to a free fermion model. The critical temperature is obtained. In special cases, we get the same results as exact solutions.     

The Critical Properties of a Modulated Quantum sine—Gordon Model

A new procedure of trial variational wave functional is proposed for invostigating the mass reuormalizationand the local structure of the ground state of a one-dimensional quantum sine-Gorrdonm model with linear spatial modu-lation, whose ground state differs from that without modulation. Thc phase diagram obtained in parameters (αA 2,β2)plane shows that the vertical part of the boundary between soliton lattice phase and iucommensurate (IC) phase withvanishing gap sticks at β2 = 4, the IC phase can only appear forβ2 ＞ 47r and thc IC phase regime is enlarged withincreasing spatial modulation in the case of definite parameter αA-2. The transition is of the continuous type on thevertical part of the boundary, while it is of the first order on the boundary forβ2 ＞ 47r.     

Critical Quantum Metrology in the Non-Linear Quantum Rabi Model

The quantum Rabi model (QRM) with linear coupling between light mode and qubit exhibits the analog of a second-order phase transition for vanishing mode frequency which allows for criticality-enhanced quantum metrology in a few-body system. We show that the QRM including a nonlinear coupling term exhibits much higher measurement precisions due to its first-order-like phase transition at finite frequency, avoiding the detrimental slowing-down effect close to the critical point of the linear QRM. When a bias term is added to the Hamiltonian, the system can be used as a fluxmeter or magnetometer if implemented in circuit QED platforms.     

Exactly Solvable Model of a Two-Level Quantum System Interacting with Spin Environment

An exactly solvable model of a two-level quantum system interacting with spin environment is considered. The interaction is assumed to be such that the state of the environment is conserved. Dynamics of the reduced density matrix of the two-level system is calculated for arbitrary coupling strength. The stationary state of the spin is obtained explicitly in the t limit.     

Critical Properties of a Quantum Hierarchical Model

A model of hierarchically interacting quantum anharmonic oscillators is considered. For this model, the sequence of abnormally normed fluctuations of the coordinate operator is shown to converge to a nontrivial thermodynamic limit when the model parameters satisfy certain conditions. This is a manifestation of the presence of a critical point for the model. Conditions on the parameters are also found which are sufficient to exclude critical points.     

Quantum Discord Behaviors in Two Qubits Spin Squeezing Model with Intrinsic Decoherence

By taking into account the intrinsic decoherence and the external magnetic field, quantum discord(QD) behaviors in two-qubit spin squeezing model are investigated in detail. It is found that the magnitude of quantum discord is strongly dependent on the initial states, the squeezing interaction μ, the magnetic field Ω and the purity r of initial states. With t → ∞, one can obtain the steady quantum discord (SQD) value, the environmental decoherence cannot entirely destroy the quantum correlation. Based on the analysis of the SQD, the conditions about the existence of SQD are obtained with different initial states. Varying the parameters μ, Ω and r not only can weaken the effects of decoherence but also can improve the magnitude of QD and SQD. The effects of the parameters μ and Ω on the QD and SQD display so different and complicated features that one cannot get an uniform law about them, while the values of QD and SQD are improved with increasing r. Properly tuning the parameters μ, Ω and r, one can obtain a larger value of QD or SQD.     

Spin Squeezing and Quantum Fisher Information in One-Axis Twisting Model with Decay

We investigate spin squeezing and the reciprocal of the mean quantum Fisher information per particle (RMQFI) of a collective spin governed by a one-axis twisting Hamiltonian with decay. In particular, we are interesting in the dependence of spin squeezing and RMQFI on the decay rate. The larger decay rate induces to stronger squeezing in certain regime and the larger period of RMQFI.     

Critical Behavior in a Quasi D Dimensional Spin Model

We study a classical spin model (more precisely a class of models) with O(N) symmetry that can be viewed as a simplified D dimensional lattice model. It is equivalent to a non-translationinvariant one dimensional model and contains the dimensionality D as a parameter that need not be an integer. The critical dimension turns out to be 2, just as in the usual translation invariant models. We study the phase structure, critical phenomena and spontaneous symmetry breaking. Furthermore we compute the perturbation expansion to low order with various boundary conditions. In our simplified models a number of questions can be answered that remain controversial in the translation invariant models, such as the asymptoticity of the perturbation expansion and the role of super-instantons. We find that perturbation theory produces the right asymptotic expansion in dimension D2 only with special boundary conditions. Finally the model allows a test of the percolation ideas of Patrascioiu and Seiler.     

Quantum Speed Limit for Dynamics of Central Spin Model with Initial System-Bath Correlations

We investigate the quantum speed limit (QSL) time of an electronic spin coupled to a bath of nuclear spins. We consider three types of initial states with different correlations between the system and bath, i.e., quantum correlation, classical correlation, and no any correlation. Interestingly, we show that the QSL times of the central spin for these three types of initial correlations are identical when the couplings are homogeneous. However, it is remarkable different for inhomogenous couplings. The QSL time of the central spin is sensitive to the initial states, the average coupling strength, the distribution of the couplings between the system and bath and the number of the nuclear spins in the bath. Furthermore, we find that the coherence in the initial state has significant influences on the QSL time of the system, and can lead to the increase of QSL time for homogeneous couplings.     

Quantum Communication in Spin Chain with Multiple Spin Exchange Interaction

The transmission of quantum states in the anisotropic Heisenberg XXZ chain model with three-spin exchange interaction is studied. The average fidelity is used to evaluate the state transfer. It is found that quantum communication can be enhanced by the anisotropic coupling and multiple spin interaction. Such spin model can reduce the time required for the perfect state transmission where the fidelity is unity. The maximally entangled Bell states can be generated and separated from the whole quantum systems.     

Spin Squeezing and Quantum Fisher Information for Mixed Hamiltonian Model

We investigate spin squeezing and the mean quantum Fisher information per particle χ ² for mixed Hamiltonian model. By adopting frozen-spin approximation, we first derive a analytical expression of spin squeezing parameter ξ ² and then numerically calculate ξ ² and χ ². It is shown that most of the time the spin squeezing appears alternatively in the x and y directions, but it cannot appear simultaneously in the two directions. It is also shown that the smaller external field strength induces better entanglement and larger period.     

Spin Squeezing and Quantum Fisher Information in the Lipkin-Meshkov-Glick Model

We investigate spin squeezing and quantum Fisher information in the Lipkin-Meshkov-Glick model. Approximate analytical expressions and the numerical analysis of spin squeezing and quantum Fisher information are derived. Spin squeezing and quantum Fisher information depend on the strength of the external transverse magnetic field and the anisotropic parameter     

Negativity and Quantum Phase Transition in the Spin Model Using the Quantum Renormalization-group Method

In this paper, we study the anisotropy parameter and Dzyaloshinskii-Moriya (DM) interaction on negativity and quantum phase transition (QPT) by using the quantum renormalization-group (QRG) method in the spin model. In our model, the anisotropy parameter and DM interaction can influence the phase diagrams. Negativity can develop two different values which separated two phases i.e. Spin-fluid phase and the Néel phase with the number of QRG iterations increased, and can obviously exhibit QPT at the critical point. Then, we find that negativity of particles 1, 3 throughout is less than negativity of particles 1, 2 or particles 2, 3. Because of information between the three particle distributions, please see the conclusion. We find that the negativity difference value (S) can also clearly detect QPT at the critical point. Most importantly, the maximum S _max become more and more close to the critical point. So S _max can be used as a criterion of the quantum phase transition occurrence when the spin chain is infinity (N → ∞).