Phase diagram of the non-hermitean asymmetric XXZ spin chain

Abstract

The low-lying excitations of the asymmetric $XXZ$ spin chain are derived explicitly in the antiferromagnetic regime through the Bethe Ansatz. It is found that a massless and conformal invariant phase with central charge $c=1$ is separated from a massive phase by a line on which the low-lying excitations surprisingly scale with the lattice length as $\Delta E\sim N^{-\frac{1}{2}}$. The mass gap vanishes with an exponent $\frac{1}{2}$ as one approaches the massless phase. The connection with the asymmetric $6$--vertex model and some physical consequences are discussed.

11 pages, latex, 1 figure in .ps format uuencoded and appended; various improvements have been made

Cited by in corpus (23)

• The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics
• Stochastic six-vertex model
• Exact Liouvillian Spectrum of a One-Dimensional Dissipative Hubbard Model
• Local scale invariance and strongly anisotropic equilibrium critical systems
• Many-body topology of non-Hermitian systems
• Universal properties of dissipative Tomonaga-Luttinger liquids: Case study of a non-Hermitian XXZ spin chain
• Breakdown of the Mott insulator: Exact solution of an asymmetric Hubbard model
• Integrability of $1D$ Lindbladians from operator-space fragmentation
• Quantum Criticality in Open Quantum Spin Chains with Nonreciprocity
• Spectra of non-hermitian quantum spin chains describing boundary induced phase transitions
• Parity-time symmetry-breaking mechanism of dynamic Mott transitions in dissipative systems
• Asymmetric XXZ chain at the antiferromagnetic transition: Spectra and partition functions
• The free energy singularity of the asymmetric 6--vertex model and the excitations of the asymmetric XXZ chain
• High-order series expansion of non-Hermitian quantum spin models
• On the construction of pseudo-hermitian quantum system with a pre-determined metric in the Hilbert space
• Spectral flow of non-hermitian Heisenberg spin chain with complex twist
• Holonomic functions of several complex variables and singularities of anisotropic Ising n-fold integrals
• Multifractality of many-body non-Hermitian skin effect
• Exactly solvable interacting vertex models
• Faceting Transition in an Exactly Solvable Terrace-Ledge-Kink model
• Direction dependent free energy singularity of the asymmetric six-vertex model
• Asymptotically exact solution of the non-Hermitian disordered interacting Hatano-Nelson chain
• R-matrix for asymmetrical XXZ spin chain in magnetic field