Time evolution of entanglement in a four-qubit Heisenberg chain

2020 ◽  
Vol 20 (9&10) ◽  
pp. 736-746
Author(s):  
Hassan Pakarzadeh ◽  
Zahra Norouzi ◽  
Javad Vahedi
Keyword(s):  
Time Evolution ◽  
Quantum Phase Transitions ◽  
Quantum Spin ◽  
Heisenberg Chain ◽  
Many Body ◽  
Quantum Spin Chain ◽  
Magnetic Systems ◽  
Dm Interaction ◽  
Werner State ◽  
Xxz Chain

The phenomenon of quantum entanglement has a very important role in quantum mechanics. Particularly, the quantum spin chain provides a platform for theoretical and experimental investigation of many-body entanglement. In this paper, we investigate time evolution of entanglement in a four-qubit anisotropic Heisenberg XXZ chain with nearest neighboring (NN), the next nearest neighboring (NNN), and the Dzialoshinskii-Moriya (DM) interactions. Calculations of the entanglement evolution of the Werner state carried out in terms of concurrence for selected ranges of control parameters such as DM interaction, frustration, etc. The results show that for the Werner state, DM interaction and the frustration parameters play important roles. Furthermore, results show that the time evolution of the Werner state entanglement may be useful to capture the quantum phase transitions in quantum magnetic systems.

scholarly journals T − W relation and free energy of the Heisenberg chain at a finite temperature

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Pengcheng Lu ◽  
Yi Qiao ◽  
Junpeng Cao ◽  
Wen-Li Yang ◽  
Kang jie Shi ◽  
...  
Keyword(s):  
Free Energy ◽  
Spin Chain ◽  
Quantum Spin ◽  
Heisenberg Chain ◽  
Quantum Spin Chain ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain ◽  
Lattice Quantum ◽  
Quantum Integrable Models ◽  
Invariant Quantum

Abstract A new nonlinear integral equation (NLIE) describing the thermodynamics of the Heisenberg spin chain is derived based on the t − W relation of the quantum transfer matrices. The free energy of the system in a magnetic field is thus obtained by solving the NLIE. This method can be generalized to other lattice quantum integrable models. Taking the SU(3)-invariant quantum spin chain as an example, we construct the corre- sponding NLIEs and compute the free energy. The present results coincide exactly with those obtained via other methods previously.

scholarly journals QUANTUM DISCORD IN THE GROUND STATE OF SPIN CHAINS

2012 ◽  
Vol 27 (01n03) ◽  
pp. 1345030 ◽  
Author(s):  
MARCELO S. SARANDY ◽  
THIAGO R. DE OLIVEIRA ◽  
LUIGI AMICO
Keyword(s):  
Ground State ◽  
Quantum Discord ◽  
Quantum Phase Transitions ◽  
Spatial Dimension ◽  
Quantum Systems ◽  
Quantum Spin ◽  
Spin Systems ◽  
Quantum Spin Systems ◽  
Quantum Spin Chain ◽  
Quantum Critical Points

The ground state of a quantum spin chain is a natural playground for investigating correlations. Nevertheless, not all correlations are genuinely of quantum nature. Here we review the recent progress to quantify the "quantumness" of the correlations throughout the phase diagram of quantum spin systems. Focusing to one spatial dimension, we discuss the behavior of quantum discord (QD) close to quantum phase transitions (QPT). In contrast to the two-spin entanglement, pairwise discord is effectively long-ranged in critical regimes. Besides the features of QPT, QD is especially feasible to explore the factorization phenomenon, giving rise to nontrivial ground classical states in quantum systems. The effects of spontaneous symmetry breaking are also discussed as well as the identification of quantum critical points through correlation witnesses.

scholarly journals INTEGRABILITY OF OPEN SPIN CHAINS WITH QUANTUM ALGEBRA SYMMETRY

1991 ◽  
Vol 06 (29) ◽  
pp. 5231-5248 ◽  
Author(s):  
LUCA MEZINCESCU ◽  
RAFAEL I. NEPOMECHIE
Keyword(s):  
Spin Chain ◽  
Quantum Algebra ◽  
Quantum Spin ◽  
Spin Chains ◽  
Invariant Chain ◽  
Quantum Spin Chain ◽  
Fundamental Representation ◽  
R Matrix ◽  
Boundary Terms ◽  
Xxz Chain

We construct an open quantum spin chain from the “twisted” [Formula: see text]R matrix in the fundamental representation which has the quantum algebra symmetry Uq[ su (2)]. This anisotropic spin-1 chain is different from the Uq[ su (2)]-invariant chain constructed from the “untwisted” [Formula: see text] spin-1 R matrix (namely, the spin-1 XXZ chain of Fateev-Zamolodchikov with boundary terms) but, nevertheless, is also completely integrable. We discuss the general case of an R matrix of the type g(k), where k∈{1, 2, 3}, and g is any simple Lie algebra.

Introduction to Integrable Many-Body Systems II

2010 ◽  
Vol 60 (2) ◽  
Author(s):  
Ladislav Šamaj
Keyword(s):  
Bethe Ansatz ◽  
Ground State ◽  
Quantum Spin ◽  
Spin Chains ◽  
Scattering Method ◽  
Heisenberg Chain ◽  
Many Body ◽  
Xxz Model ◽  
The Subject ◽  
Many Body Systems

Introduction to Integrable Many-Body Systems IIThis is the second part of a three-volume introductory course about integrable systems of interacting bodies. The models of interest are quantum spin chains with nearest-neighbor interactions between spin operators, in particular Heisenberg spin-1/2 models. The Ising model in a transverse field, expressible as a quadratic fermion form by using the Jordan-Wigner transformation, is the subject of Sect. 12. The derivation of the coordinate Bethe ansatz for the XXZ Heisenberg chain and the determination of its absolute ground state in various regions of the anisotropy parameter are presented in Sect. 13. The magnetic properties of the ground state are explained in Sect. 14. Sect. 15 concerns excited states and the zero-temperature thermodynamics of the XXZ model. The thermodynamics of the XXZ Heisenberg chain is derived on the basis of the string hypothesis in Sect. 16; the thermodynamic Bethe ansatz equations are analyzed in high-temperature and low-temperature limits. An alternative derivation of the thermodynamics without using strings, leading to a non-linear integral equation determining the free energy, is the subject of Sect. 17. A nontrivial application of the Quantum Inverse Scattering method to the fully anisotropic XYZ Heisenberg chain is described in Sect. 18. Sect. 19 deals with integrable cases of isotropic spin chains with an arbitrary spin.

scholarly journals Many-body localization in the droplet spectrum of the random XXZ quantum spin chain

2018 ◽  
Vol 275 (1) ◽  
pp. 211-258 ◽  
Author(s):  
Alexander Elgart ◽  
Abel Klein ◽  
Günter Stolz
Keyword(s):  
Spin Chain ◽  
Quantum Spin ◽  
Many Body ◽  
Quantum Spin Chain

scholarly journals SCALAR KINKS

1994 ◽  
Vol 08 (25n26) ◽  
pp. 3473-3485 ◽  
Author(s):  
H.J. DE VEGA ◽  
LUCA MEZINCESCU ◽  
RAFAEL I. NEPOMECHIE
Keyword(s):  
Spin Chain ◽  
Quantum Spin ◽  
Heisenberg Chain ◽  
Quantum Spin Chain ◽  
S Matrix ◽  
Scalar Scattering

We determine the excitations and S matrix of an integrable isotropic antiferromagnetic quantum spin chain of alternating spin 1/2 and spin 1. There are two types of gapless one-particle excitations: the usual spin 1/2 (“spinor”) kink, and a new spin 0 (“scalar”) kink. Remarkably, the scalar-spinor scattering is nontrivial, yet the spinor-spinor scattering is the same as for the Heisenberg chain. Moreover, there is no scalar-scalar scattering.

scholarly journals Interaction between Different Kinds of Quantum Phase Transitions

2021 ◽  
Vol 3 (2) ◽  
pp. 253-261
Author(s):  
Angel Ricardo Plastino ◽  
Gustavo Luis Ferri ◽  
Angelo Plastino
Keyword(s):  
Phase Transitions ◽  
Nuclear Physics ◽  
Body Problem ◽  
Quantum Phase Transitions ◽  
Quantum Phase ◽  
Exactly Solvable Models ◽  
Solvable Models ◽  
Many Body ◽  
Pairing Interaction ◽  
Exactly Solvable

We employ two different Lipkin-like, exactly solvable models so as to display features of the competition between different fermion–fermion quantum interactions (at finite temperatures). One of our two interactions mimics the pairing interaction responsible for superconductivity. The other interaction is a monopole one that resembles the so-called quadrupole one, much used in nuclear physics as a residual interaction. The pairing versus monopole effects here observed afford for some interesting insights into the intricacies of the quantum many body problem, in particular with regards to so-called quantum phase transitions (strictly, level crossings).

scholarly journals Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 984
Author(s):  
Regina Finsterhölzl ◽  
Manuel Katzer ◽  
Andreas Knorr ◽  
Alexander Carmele
Keyword(s):  
Time Evolution ◽  
Nearest Neighbor ◽  
Matrix Product ◽  
Body System ◽  
Many Body ◽  
Initial State ◽  
Matrix Product States ◽  
Open Quantum ◽  
Many Body Systems ◽  
The Many

This paper presents an efficient algorithm for the time evolution of open quantum many-body systems using matrix-product states (MPS) proposing a convenient structure of the MPS-architecture, which exploits the initial state of system and reservoir. By doing so, numerically expensive re-ordering protocols are circumvented. It is applicable to systems with a Markovian type of interaction, where only the present state of the reservoir needs to be taken into account. Its adaption to a non-Markovian type of interaction between the many-body system and the reservoir is demonstrated, where the information backflow from the reservoir needs to be included in the computation. Also, the derivation of the basis in the quantum stochastic Schrödinger picture is shown. As a paradigmatic model, the Heisenberg spin chain with nearest-neighbor interaction is used. It is demonstrated that the algorithm allows for the access of large systems sizes. As an example for a non-Markovian type of interaction, the generation of highly unusual steady states in the many-body system with coherent feedback control is demonstrated for a chain length of N=30.

scholarly journals Quantum spin chain dissipative mean-field dynamics

2018 ◽  
Vol 51 (32) ◽  
pp. 325001 ◽  
Author(s):  
F Benatti ◽  
F Carollo ◽  
R Floreanini ◽  
H Narnhofer
Keyword(s):  
Spin Chain ◽  
Mean Field ◽  
Quantum Spin ◽  
Quantum Spin Chain
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