XY Model In Transverse Field Research Articles

Concurrence distribution in excited states of the one-dimensional spin-1/2 transverse-field XY model: Two different regions.

We investigate the variation of concurrence in a spin-1/2 transverse field XY chain system in an excited state. Initially, we precisely solve the eigenvalue problem of the system Hamiltonian using the fermionization technique. Subsequently, we calculate the concurrence between nearest-neighbor pairs of spins in all excited states with higher energy than the ground state. Below the factorized field, denoted as h_{f}=sqrt[J^{2}-(Jδ)^{2}], we find no pairwise entanglement between nearest neighbors in excited states. At the factorized field, corresponding to a factorized state, we observe weak concurrence in very low energy states. Beyond h_{f}, the concurrence strengthens, entangling all excited states. The density of entangled states peaks at the center of the excited spectrum. Additionally, the distribution of concurrence reveals that the midpoint of the nonzero concurrence range harbors the most entangled excited states.

Controlling gain with loss: Bounds on localizable entanglement in multiqubit systems

We investigate the relation between the amount of entanglement localized on a chosen subsystem of a multiqubit system via local measurements on the rest of the system, and the bipartite entanglement that is lost during this measurement process. We study a number of paradigmatic pure states, including the generalized Greenberger--Horne--Zeilinger (GHZ), the generalized $W$ (gW), Dicke, and the generalized Dicke states. For the generalized GHZ and $W$ states, we analytically derive bounds on localizable entanglement in terms of the entanglement present in the system prior to the measurement. Also, for the Dicke and the generalized Dicke states, we demonstrate that with increasing system size, localizable entanglement tends to be equal to the bipartite entanglement present in the system over a specific partition before measurement. We extend the investigation numerically in the case of arbitrary multiqubit pure states. We also analytically determine the modification of these results, including the proposed bounds, in situations where these pure states are subjected to single-qubit phase-flip noise on all qubits. Additionally, we study one-dimensional paradigmatic quantum spin models, namely, the transverse-field XY model and the XXZ model in an external field, and numerically demonstrate a cubic dependence of the localized entanglement on the lost entanglement. We show that this relation is robust even in the presence of disorder in the strength of the external field.

Information scrambling and redistribution of quantum correlations through dynamical evolution in spin chains

We investigate the propagation of local bipartite quantum correlations, along with the tripartite mutual information to characterize the information scrambling through dynamical evolution of spin chains. Starting from an initial state with the first pair of spins in a Bell state, we study how quantum correlations spread to other parts of the system, using different representative spin Hamiltonians, viz. the Heisenberg Model, a spin-conserving model, the transverse-field XY model, a non-conserving but integrable model, and the kicked Harper model, a spin conserving but nonintegrable model. We show that the local correlations spread consistently in the case of spin-conserving dynamics in both integrable and nonintegrable cases, with a strictly nonnegative tripartite mutual information. In contrast, in the case of non-conserving dynamics, tripartite mutual information is negative and local pair correlations do not propagate.

The transverse field XY model on the diamond chain

We consider the s=1/2 transverse field XY model on the frustrated diamond chain, considering anisotropic exchange parameters between nearest neighbor spins. To this end, we employ three different methodologies: mean-field approximations, and state-of-the-art exact diagonalizations (ED), and density matrix renormalization group (DMRG) simulations. Within a mean-field theory, the Hamiltonian is fermionized by introducing the Jordan–Wigner transformation, and the interacting (many-body) terms are approximated to single-particle ones by a Hartree–Fock approach. We analyze the behavior of the induced and spontaneous magnetization as functions of the external field, investigating the magnetic properties at the ground state, and at finite temperatures. Interestingly, the mean-field results are in reasonable agreement with the ED and DMRG ones, in particular for the distorted chain, or at an intermediate/large spin anisotropy parameter. As our key results, we present phase diagrams anisotropy × magnetic field at zero temperature, discussing the emergence of phases and its quantum critical points. Finally, our analysis at finite temperature provides a range of parameters in which an unusual behavior of the induced magnetization occurs — with it increasing as a function of temperature. This work presents a global picture of the XY model on the diamond chain, which may be useful to understand features of magnetism in more complex geometries.

Steered Quantum Coherence and Quantum Criticality in the XY Model with Dzyaloshinsky–Moriya Interaction

The critical behaviors of the steered quantum coherence (SQC) in the transverse field XY model with Dzyaloshinsky–Moriya (DM) interaction are explored. It is found that there is an inflexion for the SQC at the critical field of quantum phase transition (QPT) for two long‐distance spins, and there is a divergence for the derivative of the SQC with respect to the magnetic field at the critical field of QPT for any two spins in the chain. Moreover, SQC shows distinct behaviors in different phase regions of the model, which is also a signature of the QPT. Furthermore, the SQC method is robust in studying quantum criticality even under environmental coupling.

Multicritical behavior of the fidelity susceptibility for the 2D quantum transverse-field XY model

The two-dimensional quantum $XY$ model with a transverse magnetic field was investigated with the exact diagonalization method. Upon turning on the magnetic field $h$ and the $XY$-plane anisotropy $\eta$, there appear a variety of phase boundaries, which meet at the multicritical point $(h,\eta)=(2,0)$. We devote ourselves to the Ising-universality branch, placing an emphasis on the multicritical behavior. As a probe to detect the underlying phase transitions, we adopt the fidelity susceptibility $\chi_F$. The fidelity susceptibility does not rely on any presumptions as to the order parameter involved. We made a finite-size-scaling analysis of $\chi_F$ for $\eta=1$ (Ising limit), where a number of preceding results are available. Thereby, similar analyses with $\eta$ scaled were carried out around the multicritical point. We found that the $\chi_F$ data are described by the crossover scaling theory. A comparison with the preceding studies of the multicriticality is made.

Markovian and Non-Markovian Dynamics in the One-Dimensional Transverse-Field XY Model

We consider an anisotropic spin-1/2 XY Heisenberg chain in the presence of a transverse magnetic field. Selecting the nearest neighbor pair spins as an open quantum system, the rest of the chain plays the role of the structured environment. In fact, the aforementioned system is used as a quantum probe signifying nontrivial features of the environment with which is interacting. We use a general measure that is based on the trace distance for the degree of non-Markovian behavior in open quantum systems. The witness of non-Markovianity takes on nonzero values whenever there is a flow of information from the environment back to the open system. We have shown that the dynamics of the system with isotropic Heisenberg interaction is Markovian. A dynamical transition into the non-Markovian regime is observed as soon as the anisotropy, $$\gamma $$ , is applied. At the Ising value of the anisotropy $$\gamma =1.0$$ , all the information flows back from the environment to the system. The additional dynamical transition from the non-Markovian to the Markovian is obtained by applying the transverse magnetic field. In addition, we have focused on the time evolution of the Loschmidt-echo return rate function. It is found that a non-analyticity can be seen in the time evolution of the Loschmidt-echo return rate function exactly at the critical points where a dynamical transition from the Markovian to the non-Markovian occurs.

Quantum stabilization of photonic spatial correlations

The driven, dissipative Bose–Hubbard model (BHM) provides a generic description of collective phases of interacting photons in cavity arrays. In the limit of strong optical nonlinearities (hard-core limit), the BHM maps on the dissipative, transverse-field XY model (XYM). The steady-state of the XYM can be analyzed using mean-field theory, which reveals a plethora of interesting dynamical phenomena. For example, strong hopping combined with a blue-detuned drive, leads to an instability of the homogeneous steady-state with respect to antiferromagnetic fluctuations. In this paper, we address the question whether such an antiferromagnetic instability survives in the presence of quantum correlations beyond the mean-field approximation. For that purpose, we employ a self-consistent 1/z expansion for the density matrix, where z is the lattice coordination number, i.e. the number of nearest neighbors for each site. We show that quantum fluctuations stabilize a new homogeneous steady-state with antiferromagnetic correlations in agreement with exact numerical simulations for finite lattices. The latter manifests itself as short-ranged oscillations of the first and second-order spatial coherence functions of the photons emitted by the array.

Signatures of topological quantum phase transitions in driven and dissipative qubit arrays

We study photonic signatures of symmetry broken and topological phases in a driven, dissipative circuit QED realization of spin-1/2 chains. Specifically, we consider the transverse-field XY model and a dual model with 3-spin interactions. The former has a ferromagnetic and a paramagnetic phase, while the latter features, in addition, a symmetry protected topological phase. Using the method of third quantization, we calculate the non-equilibrium steady-state of the open spin chains for arbitrary system sizes and temperatures. We find that the bi-local correlation function of the spins at both ends of the chain provides a sensitive measure for both symmetry-breaking and topological phase transitions of the systems, but no universal means to distinguish between the two types of transitions. Both models have equivalent representations in terms of free Majorana fermions, which host zero, one and two topological Majorana end modes in the paramagnetic, ferromagnetic, and symmetry protected topological phases, respectively. The correlation function we study retains its bi-local character in the fermionic representation, so that our results are equally applicable to the fermionic models in their own right. We propose a photonic realization of the dissipative transverse-field XY model in a tunable setup, where an array of superconducting transmon qubits is coupled at both ends to a photonic microwave circuit.

QUANTUM DISCORD, DECOHERENCE AND QUANTUM PHASE TRANSITION

Quantum discord is a more general measure of quantum correlations than entanglement and has been proposed as a resource in certain quantum information processing tasks. The computation of discord is mostly confined to two-qubit systems for which an analytical calculational scheme is available. The utilization of quantum correlations in quantum information-based applications is limited by the problem of decoherence, i.e., the loss of coherence due to the inevitable interaction of a quantum system with its environment. The dynamics of quantum correlations due to decoherence may be studied in the Kraus operator formalism for different types of quantum channels representing system-environment interactions. In this review, we describe the salient features of the dynamics of classical and quantum correlations in a two-qubit system under Markovian (memoryless) time evolution. The two-qubit state considered is described by the reduced density matrix obtained from the ground state of a spin model. The models considered include the transverse-field XY model in one dimension, a special case of which is the transverse-field Ising model, and the XXZ spin chain. The quantum channels studied include the amplitude damping, bit-flip, bit-phase-flip and phase-flip channels. The Kraus operator formalism is briefly introduced and the origins of different types of dynamics discussed. One can identify appropriate quantities associated with the dynamics of quantum correlations which provide signatures of quantum phase transitions in the spin models. Experimental observations of the different types of dynamics are also mentioned.

QUANTUM DISCORD IN A SPIN SYSTEM WITH SYMMETRY BREAKING

We analyze the quantum discordQ throughout the low temperature phase diagram of the quantum XY model in transverse field. We first focus on the T = 0 order–disorder quantum phase transition QPT both in the symmetric ground state and in the symmetry broken one. Beside it, we highlight how Q displays clear anomalies also at a noncritical value of the control parameter inside the ordered phase, where the ground state is completely factorized. We evidence how the phenomenon is in fact of collective nature and displays universal features. We also study Q at finite temperature. We show that, close to the QPT, Q exhibits quantum-classical crossover of the system with universal scaling behavior. We evidence a nontrivial pattern of thermal correlations resulting from the factorization phenomenon.

Markovian evolution of classical and quantum correlations in transverse-field XY model

The transverse-field XY model in one dimension is a well-known spin model for which the ground state properties and excitation spectrum are known exactly. The model has an interesting phase diagram describing quantum phase transitions (QPTs) belonging to two different universality classes. These are the transverse-field Ising model and the XX model universality classes with both the models being special cases of the transverse-field XY model. In recent years, quantities related to quantum information theoretic measures like entanglement, quantum discord (QD) and fidelity have been shown to provide signatures of QPTs. Another interesting issue is that of decoherence to which a quantum system is subjected due to its interaction, represented by a quantum channel, with an environment. In this paper, we determine the dynamics of different types of correlations present in a quantum system, namely, the mutual information, the classical correlations and the quantum correlations, as measured by the quantum discord, in a two-qubit state. The density matrix of this state is given by the nearest-neighbour reduced density matrix obtained from the ground state of the transverse-field XY model in 1d. We assume Markovian dynamics for the time-evolution due to system-environment interactions. The quantum channels considered include the bit-flip, bit-phase-flip and phase-flip channels. Two different types of dynamics are identified for the channels in one of which the quantum correlations are greater in magnitude than the classical correlations in a finite time interval. The origins of the different types of dynamics are further explained. For the different channels, appropriate quantities associated with the dynamics of the correlations are identified which provide signatures of QPTs. We also report results for further-neighbour two-qubit states and finite temperatures.

Scaling of reduced fidelity susceptibility in the one-dimensional transverse-field XY model

We show that the reduced fidelity susceptibility in the family of one-dimensional XY model obeys scaling behavior in the vicinity of quantum critical points both analytically and numerically. The logarithmic divergence behavior suggests that the reduced fidelity susceptibility can act as an indicator of quantum phase transition.

Density of states in 1D S=1/2 anisotropic XY model with random parameters

Abstract The determination of the spectrum of the Hamiltonian for 1D s= 1/2 anisotropic nonuniform XY model in transverse field reduces to the determination of the eigenvalues of dynamical matrix for 1D nonuniform chain within harmonic approximation taking into account the interactions between nearest and next nearest neighbours. Therefore Dean's method may be used for finding the density of states. The obtained in such a manner result for isotropic XY model in lorentzian random transverse field, for which an exact result is known, is discussed.

1D S = 1/2 anisotropic xy model in transverse field with dzyaloshinskii-moriya interaction

Abstract Using Jordan-Wigner fermionization we examined the statistical mechanics of 1D s=1/2 XY model in transverse field with Dzyaloshinskii-Moriya interaction. In particular we calculated exactly the transverse dynamical susceptibility. The obtained results change dramatically in the presence of Dzyaloshinskii-Moriya interaction that can be of considerable interest in connection with the corresponding experimental studies.

Statistical mechanics of one-dimensional S=1/2 anisotropic XY model in transverse field with Dzyaloshinskii-Moriya interaction

Statistical mechanics of one-dimensional S=1/2 anisotropic XY model in transverse field with Dzyaloshinskii-Moriya interaction