Form Factors of the Heisenberg Spin Chain in the Thermodynamic Limit: Dealing with Complex Bethe Roots

In this article we study the thermodynamic limit of the form factors of the XXX Heisenberg spin chain using the algebraic Bethe ansatz approach. Our main goal is to express the form factors for the low-lying excited states as determinants of matrices that remain finite dimensional in the thermodynamic limit. We show how to treat all types of the complex roots of the Bethe equations within this framework. In particular we demonstrate that the Gaudin determinant for the higher level Bethe equations arises naturally from the algebraic Bethe ansatz.

Nonequilibrium steady states in the Floquet-Lindblad systems: van Vleck's high-frequency expansion approach

Nonequilibrium steady states (NESSs) in periodically driven dissipative quantum systems are vital in Floquet engineering. We develop a general theory for high-frequency drives with Lindblad-type dissipation to characterize and analyze NESSs. This theory is based on the high-frequency (HF) expansion with linear algebraic numerics and without numerically solving the time evolution. Using this theory, we show that NESSs can deviate from the Floquet-Gibbs state depending on the dissipation type. We also show the validity and usefulness of the HF-expansion approach in concrete models for a diamond nitrogen-vacancy (NV) center, a kicked open XY spin chain with topological phase transition under boundary dissipation, and the Heisenberg spin chain in a circularly-polarized magnetic field under bulk dissipation. In particular, for the isotropic Heisenberg chain, we propose the dissipation-assisted terahertz (THz) inverse Faraday effect in quantum magnets. Our theoretical framework applies to various time-periodic Lindblad equations that are currently under active research.

How to Draw a Correlation Function

We discuss connection between the XX0 Heisenberg spin chain and some aspects of enumerative combinatorics. The representation of the Bethe wave functions via the Schur functions allows to apply the theory of symmetric functions to the calculation of the correlation functions. We provide a combinatorial derivation of the dynamical auto-correlation functions and visualise them in terms of nests of self-avoiding lattice paths. Asymptotics of the auto-correlation functions are obtained in the double scaling limit provided that the evolution parameter is large.

Generation of spin currents by a temperature gradient in a two-terminal device

Theoretical and experimental studies of the interaction between spins and temperature are vital for the development of spin caloritronics, as they dictate the design of future devices. In this work, we propose a two-terminal cold-atom simulator to study that interaction. The proposed quantum simulator consists of strongly interacting atoms that occupy two temperature reservoirs connected by a one-dimensional link. First, we argue that the dynamics in the link can be described using an inhomogeneous Heisenberg spin chain whose couplings are defined by the local temperature. Second, we show the existence of a spin current in a system with a temperature difference by studying the dynamics that follows the spin-flip of an atom in the link. A temperature gradient accelerates the impurity in one direction more than in the other, leading to an overall spin current similar to the spin Seebeck effect.

Thermal correlations and entropic uncertainty in a two-spin system under DM and KSEA interactions

In this paper, the thermal quantum correlations along with the thermal entropic uncertainty in a two neighboring XYZ Heisenberg spin-1/2 particles subjected to a transverse external magnetic field with the interplay of both antisymmetric Dzyaloshinskii–Moriya and symmetric Kaplan–Shekhtman–Entin–Wohlman–Aharony are investigated. The quantum consonance and uncertainty-induced quantum nonlocality as well as the entropic uncertainty with quantum memory for the considered system are specified and the thermal behaviors of them in terms of the system parameters are examined. The expected decrease of quantum correlations for higher absolute temperatures is confirmed while the inflation of the uncertainty is generated. Moreover, we show that the stronger spin-spin and spin-orbit exchange couplings can enhance the thermal quantum correlations and suppress the uncertainty. Accordingly, our remarks are expected to be beneficent in illustrating the dynamical quantum correlations and entropy-based uncertainty in a general Heisenberg spin-chain model and thus would be useful for practical quantum information processing.

The Yangian relations of Heisenberg spin chain model

In this paper, we investigate the Yangian relations of Heisenberg spin chain systems. Firstly, we consider the closed XXZ spin chain model, through the Heisenberg spin XXZ model, we found the Hamiltonians for one kind system of three adjacent partial particles interaction systems. The model’s constitution rules of energy levels and energy states which expand from the few-particle system to multi-particle system have good regularity. In this system, we found Yangian’s law and illustrate it through graphs. Secondly, we further consider the closed XXZ spin chain’s generalization of other three neighboring particles interaction systems from few-particle system to multi-particle system. Finally, we also discussed the laws of the three adjacent particles system of some models, they are the XXZ model with twist boundary condition, the open XXZ spin chain model and the XXZ model containing the next neighbor. In addition, not only XXZ model, XXX model, XY model and Ising model, but the relevant laws of spin-1 systems of these models were also discussed, they have similar rules to the XXZ model. Through calculation and research, the eigensystems of these models all have good Yangian and constitution laws.

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

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.