scholarly journals Stochastic dissipative quantum spin chains (I) : Quantum fluctuating discrete hydrodynamics

2017 ◽  
Vol 3 (5) ◽  
Author(s):  
Michel Bauer ◽  
Denis Bernard ◽  
Tony Jin
Keyword(s):  
Spin Chain ◽  
Quantum Dynamics ◽  
Quantum Noise ◽  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Spin Chains ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain ◽  
Dissipative Effects ◽  
Macroscopic Fluctuation Theory

Motivated by the search for a quantum analogue of the macroscopic fluctuation theory, we study quantum spin chains dissipatively coupled to quantum noise. The dynamical processes are encoded in quantum stochastic differential equations. They induce dissipative friction on the spin chain currents. We show that, as the friction becomes stronger, the noise induced dissipative effects localize the spin chain states on a slow mode manifold, and we determine the effective stochastic quantum dynamics of these slow modes. We illustrate this approach by studying the quantum stochastic Heisenberg spin chain.

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 Magnetic field tuning of quantum spin excitations in a weakly coupled S=12 Heisenberg spin chain as seen from NMR

2019 ◽  
Vol 100 (12) ◽  
Author(s):  
Long Ma ◽  
Z. Wang ◽  
L. Hu ◽  
Z. Qu ◽  
N. Hao ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Spin Chain ◽  
Quantum Spin ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain ◽  
Weakly Coupled ◽  
Spin Excitations

scholarly journals Quantum spin transistor with a Heisenberg spin chain

2016 ◽  
Vol 7 (1) ◽  
Author(s):  
O. V. Marchukov ◽  
A. G. Volosniev ◽  
M. Valiente ◽  
D. Petrosyan ◽  
N. T. Zinner
Keyword(s):  
Spin Chain ◽  
Quantum Spin ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain ◽  
Spin Transistor

scholarly journals Shift-invert diagonalization of large many-body localizing spin chains

2018 ◽  
Vol 5 (5) ◽  
Author(s):  
Francesca Pietracaprina ◽  
Nicolas Macé ◽  
David J. Luitz ◽  
Fabien Alet
Keyword(s):  
Random Field ◽  
Linear Algebra ◽  
Spin Chain ◽  
Quantum Systems ◽  
Exact Diagonalization ◽  
Spin Chains ◽  
Many Body ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain ◽  
Sparse Linear Algebra

We provide a pedagogical review on the calculation of highly excited eigenstates of disordered interacting quantum systems which can undergo a many-body localization (MBL) transition, using shift-invert exact diagonalization. We also provide an example code at https://bitbucket.org/dluitz/sinvert_mbl. Through a detailed analysis of the simulational parameters of the random field Heisenberg spin chain, we provide a practical guide on how to perform efficient computations. We present data for mid-spectrum eigenstates of spin chains of sizes up to L=26L=26. This work is also geared towards readers with interest in efficiency of parallel sparse linear algebra techniques that will find a challenging application in the MBL problem.

A TEMPLATE FOR QUANTUM SPIN CHAIN SPECTRA

1992 ◽  
Vol 07 (supp01b) ◽  
pp. 707-730 ◽  
Author(s):  
PAUL MARTIN ◽  
VLADIMIR RITTENBERG
Keyword(s):  
Spin Chain ◽  
Hecke Algebra ◽  
Quantum Spin ◽  
Spin Chains ◽  
Irreducible Representations ◽  
Quantum Spin Chains ◽  
Young Diagrams ◽  
Quantum Spin Chain ◽  
Fixed Length

We consider a series of N-state L(≥N) site quantum spin chains, characterised by the ordered partition of N into 2 parts, N=P+M. These (P/M) chains are invariant under an action of UqSU(P/M), and are built from a representation of the Hecke algebra HL-1(q). We establish that the intersection of the spectra of a (P/M) and (P'/M') chain of fixed length L is the spectrum of the (min(P,P')/min(M,M')) chain of that length. We establish that the spectrum of the (P/M) chain breaks into blocks corresponding to irreducible representations of HL-1(q) (or equivalently irreducible representations of UqSU(P/M)) characterised by Young diagrams with no rectangular subdiagrams of dimension (P+1)×(M+1) (height × width resp.). We give the corresponding quotient relations for the Hecke algebra. We discuss several implications of these results.

CORRELATION FUNCTIONS IN QUANTUM SPIN CHAINS AND VERTEX MODELS

2001 ◽  
Vol 16 (11) ◽  
pp. 1875-1887
Author(s):  
VIERI MASTROPIETRO
Keyword(s):  
Correlation Functions ◽  
Spin Chain ◽  
Nearest Neighbor ◽  
Quantum Spin ◽  
Spin Chains ◽  
Vertex Model ◽  
Quantum Spin Chains ◽  
Neighbor Interaction ◽  
Vertex Models

Some correlation functions of critical models, like the anisotropic spin chain with nearest and next-to-nearest neighbor interaction, or the eight vertex model, are computed as a corollary of the study of the XYZ model in [2].

scholarly journals Lattice Bisognano-Wichmann modular Hamiltonian in critical quantum spin chains

2020 ◽  
Vol 2 (2) ◽  
Author(s):  
Jiaju Zhang ◽  
Pasquale Calabrese ◽  
Marcello Dalmonte ◽  
Mohammad Ali Rajabpour
Keyword(s):  
Correlation Functions ◽  
Spin Chain ◽  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Spin Chains ◽  
Density Matrices ◽  
Reduced Density Matrices ◽  
Trace Distance ◽  
The Difference ◽  
Reduced Density

We carry out a comprehensive comparison between the exact modular Hamiltonian and the lattice version of the Bisognano-Wichmann (BW) one in one-dimensional critical quantum spin chains. As a warm-up, we first illustrate how the trace distance provides a more informative mean of comparison between reduced density matrices when compared to any other Schatten nn-distance, normalized or not. In particular, as noticed in earlier works, it provides a way to bound other correlation functions in a precise manner, i.e., providing both lower and upper bounds. Additionally, we show that two close reduced density matrices, i.e. with zero trace distance for large sizes, can have very different modular Hamiltonians. This means that, in terms of describing how two states are close to each other, it is more informative to compare their reduced density matrices rather than the corresponding modular Hamiltonians. After setting this framework, we consider the ground states for infinite and periodic XX spin chain and critical Ising chain. We provide robust numerical evidence that the trace distance between the lattice BW reduced density matrix and the exact one goes to zero as \ell^{-2}ℓ−2 for large length of the interval \ellℓ. This provides strong constraints on the difference between the corresponding entanglement entropies and correlation functions. Our results indicate that discretized BW reduced density matrices reproduce exact entanglement entropies and correlation functions of local operators in the limit of large subsystem sizes. Finally, we show that the BW reduced density matrices fall short of reproducing the exact behavior of the logarithmic emptiness formation probability in the ground state of the XX spin chain.

Solvable nineteen-vertex models and quantum spin chains of spin one

1994 ◽  
Vol 4 (8) ◽  
pp. 1151-1159 ◽  
Author(s):  
Makoto Idzumi ◽  
Tetsuji Tokihiro ◽  
Masao Arai
Keyword(s):  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Spin Chains ◽  
Vertex Models

scholarly journals Slow Propagation in Some Disordered Quantum Spin Chains

2021 ◽  
Vol 182 (1) ◽  
Author(s):  
Bruno Nachtergaele ◽  
Jake Reschke
Keyword(s):  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Spin Chains ◽  
Slow Propagation
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