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arXiv:2301.11896 · SciPost Physics

Scale-free non-Hermitian skin effect in a boundary-dissipated spin chain

He-Ran Wang, Bo Li, Fei Song, Zhong Wang

Published Nov 13, 2023• 24 citations
arXivHTMLPDF

Abstract

We study the open XXZ spin chain with a PT P T -symmetric non-Hermitian boundary field. We find an interaction-induced scale-free non-Hermitian skin effect by using the coordinate Bethe Ansatz. The steady-state and the ground state in the PT P T broken phase are constructed, and the formulas of their eigen-energies in the thermodynamic limit are obtained. The differences between the many-body scale-free states and the boundary string states are explored, and the transition between the two at the isotropic point is investigated. We also discuss an experimental scheme to verify our results.

DOI
10.21468/scipostphys.15.5.191

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We study the open XXZ spin chain with a PT P T -symmetric non-Hermitian boundary field. We find an interaction-induced scale-free non-Hermitian skin effect by using the coordinate Bethe Ansatz. The steady-state and the ground state in the PT P T broken phase are constructed, and the formulas of their eigen-energies in the thermodynamic limit are obtained. The differences between the many-body scale-free states and the boundary string states are explored, and the transition between the two at the isotropic point is investigated. We also discuss an experimental scheme to verify our results.
The authors construct here an exactly solvable \ensuremath{\mathcal{P}}\ensuremath{\mathcal{T}}-symmetric non-Hermitian Heisenberg spin chain with complex-conjugate boundary Kondo couplings. They show that the model exhibits three distinct boundary phases: dissipative Kondo screening with unbroken \ensuremath{\mathcal{P}}\ensuremath{\mathcal{T}} symmetry, bound-mode phases featuring spontaneously broken \ensuremath{\mathcal{P}}\ensuremath{\mathcal{T}} symmetry and complex-conjugate eigenvalues, and an unscreened local-moment phase with a purely real spectrum. Benchmarking with non-Hermitian DMRG demonstrates quantitative agreement with Bethe ansatz, validating tensor-network methods for open quantum systems.
Abstract We construct the exact solution of a non-Hermitian P T -symmetric isotropic Heisenberg spin chain with integrable boundary fields. We find that the system exhibits two types of phases named A and B . In the B type phase, the P T symmetry remains unbroken and it comprises of eigenstates with only real energies, whereas the A type phase exhibits both P T symmetry broken and unbroken sectors, comprising of eigenstates with only complex and real energies respectively. The P T -symmetry broken sector comprises of pairs of eigenstates whose energies are complex conjugates of each other. The existence of two sectors in the A type phase is associated with the exponentially localized bound states at the edges with complex energies which are described by boundary strings. We find that both A and B type phases can be further divided into sub-phases which exhibit different ground states. We also compute the bound state wavefunction in one magnon sector and find that as the imaginary value of the boundary parameter is increased, the exponentially localized wavefunction broadens thereby protruding more into the bulk, which indicates that exponentially localized bound states may not be stabilized for large imaginary values of the boundary parameter.
The thermodynamic limit and boundary energy of the isotropic spin-1 Heisenberg chain with non-diagonal boundary fields are studied. The finite size scaling properties of the inhomogeneous term in the T-Q relation at the ground state are calculated by the density matrix renormalization group. Based on our findings, the boundary energy of the system in the thermodynamic limit can be obtained from Bethe ansatz equations of a related model with parallel boundary fields. These results can be generalized to the SU(2) symmetric high spin Heisenberg model directly.
A bstract We study the thermodynamic limit of the anisotropic XYZ spin chain with non-diagonal integrable open boundary conditions. Although the U(1)-symmetry is broken, by using the new parametrization scheme, we exactly obtain the surface energy and the excitation energy of the system, which has solved the difficulty in the inhomogeneous T − Q relation. With the boundary parameters in the regions making the Hamiltonian Hermitian, we have obtained the distribution patterns of the zeros of the eigenvalue of the transfer matrix for the ground state and the excited ones. We find that the surface and excitation energies depend on the parities of sites number N , due to the long-range Neel order in the bulk. The easy-axis and thermodynamic limit for all the regions of boundary parameters are studied. We also obtain the physical quantities in the thermodynamic limit of boundary XXZ model by taking the trigonometric limit.
The non-Hermitian skin effect, in which eigenstates of non-Hermitian Hamiltonians are localized at one boundary in the open boundary condition, has attracted great interest recently. In this paper, we investigate the skin effect in one-dimensional dissipative quantum many-body systems, which we call the Liouvillian skin effect (LSE). We rigorously identify the existence of the LSE for generalized boundary conditions by solving the Liouvillian superoperator of an exactly solvable model with the advantage of the Bethe ansatz. The LSE is sensitive to boundary conditions where the signature is reflected in eigenfunctions of the system. We confirm that the LSE is fragile to a tiny coflow boundary hopping with non-Hermitian current but can survive a counterflow boundary hopping in the thermodynamic limit. Our work provides a prototypical example of exactly solvable dissipative quantum many-body lattice systems exhibiting the LSE for generalized boundary conditions. It can be further extended to other integrable open quantum many-body models.
We propose a novel type of skin effects in non-Hermitian quantum many-body systems that we dub a "non-Hermitian Mott skin effect." This phenomenon is induced by the interplay between strong correlations and the non-Hermitian point-gap topology. The Mott skin effect induces extreme sensitivity to the boundary conditions only in the spin degree of freedom (i.e., the charge distribution is not sensitive to boundary conditions), which is in sharp contrast to the ordinary non-Hermitian skin effect in noninteracting systems. Concretely, we elucidate that a bosonic non-Hermitian chain exhibits the Mott skin effect in the strongly correlated regime by closely examining an effective Hamiltonian. The emergence of the Mott skin effect is also supported by numerical diagonalization of the bosonic chain. The difference between the ordinary non-Hermitian skin effect and the Mott skin effect is also reflected in the time evolution of physical quantities; under the time evolution spin accumulation is observed while the charge distribution remains spatially uniform.