A spin chain with non-Hermitian symmetric boundary couplings: exact solution, dissipative Kondo effect, and phase transitions on the edge
arXiv:2406.10334 · doi:10.1103/PhysRevB.111.224407
Abstract
We construct an exactly solvable symmetric non-Hermitian model where a spin isotropic quantum Heisenberg spin chain is coupled to two spin Kondo impurities at its boundaries with coupling strengths that are complex conjugates of each other. Solving the model by means of a combination of the Bethe Ansatz and density matrix renormalization group (DMRG) techniques, we show that the model exhibits three distinct boundary phases: a symmetric phase with a dissipative Kondo effect, a phase with bound modes and spontaneously broken symmetry, and a phase with an effectively unscreened spin (i.e. a free local moment). In the Kondo and the unscreened phases, the symmetry is unbroken, and hence all states have real energies, whereas in the bound mode phases, in addition to the states with real energies, there exist states with complex energy eigenvalues that appear in complex conjugate pairs, signaling spontaneous breaking of the symmetry. The exact solution is used to provide an accessible benchmark for DMRG with a non-Hermitian matrix product operator representation that demonstrates an accuracy comparable to its Hermitian limit thus showing the power of DMRG to handle non-Hermitian many body calculations.
arXiv comment11 pages (and 15 pages appendices) and 12+7 figures
References in corpus (48)
- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
- Non-Hermitian Physics
- The ITensor Software Library for Tensor Network Calculations
- Excitations in a non-equilibrium Bose-Einstein condensate of exciton-polaritons
- A short introduction to the Lindblad Master Equation
- Third quantization: a general method to solve master equations for quadratic open Fermi systems
- Exact PT-Symmetry Is Equivalent to Hermiticity
- Entanglement transition in a monitored free fermion chain -- from extended criticality to area law
- Observation of a dissipative phase transition in a one-dimensional circuit QED lattice
- Spin transport in a tunable Heisenberg model realized with ultracold atoms
- Extension of PT-Symmetric Quantum Mechanics to Quantum Field Theory with Cubic Interaction
- PT Metamaterials via Complex-Coordinate Transformation Optics
- Non-Hermitian Kondo effect in ultracold alkaline-earth atoms
- Parity-time-symmetric topological superconductor
- Exact Bethe ansatz spectrum of a tight-binding chain with dephasing noise
- Observation of PT-symmetric quantum interference
- Quantum jumps in the non-Hermitian dynamics of a superconducting qubit
- Symmetric Real Dirac Fermions and Semimetals
- Surface excitations and surface energy of the antiferromagnetic XXZ chain by the Bethe ansatz approach
- Universal properties of dissipative Tomonaga-Luttinger liquids: Case study of a non-Hermitian XXZ spin chain
- Quantum correlations near the exceptional point
- Engineered dissipation induced entanglement transition in quantum spin chains: from logarithmic growth to area law
- Probing Complex-energy Topology via Non-Hermitian Absorption Spectroscopy in a Trapped Ion Simulator
- Quantum simulation of parity-time symmetry breaking with a superconducting quantum processor
- Exact solution of the open Heisenberg chain with two impurities
- Functional Bethe ansatz methods for the open XXX chain
- Non-Hermitian strongly interacting Dirac fermions: a quantum Monte-Carlo study
- Calculation of the Hidden Symmetry Operator for a $\cP\cT$-Symmetric Square Well
- PT Symmetric Floquet Topological Phase in SSH Model
- Understanding Hawking radiation in the framework of open quantum systems
- Kondo Effect in Spin Chains
- Interaction Control of Ultracold Alkaline-Earth Atoms
- Non-Hermitian Hamiltonian for a Modulated Jaynes-Cummings Model with PT Symmetry
- Dissipative spin chains: Implementation with cold atoms and steady-state properties
- Is the concept of the non-Hermitian effective Hamiltonian relevant in the case of potential scattering?
- Hot Cosmic Qubits: Late-Time de Sitter Evolution and Critical Slowing Down
- Kondo impurity at the edge of a superconducting wire
- Exact solution of a non-Hermitian -symmetric Heisenberg spin chain
- Rise and fall of Yu-Shiba-Rusinov bound-states in charge conserving -wave one-dimensional superconductors
- Dissipation driven phase transition in the non-Hermitian Kondo model
- Signature of PT-symmetric non-Hermitian superconductivity in angle-resolved photoelectron fluctuation spectroscopy
- Kondo effect in the isotropic Heisenberg spin chain
- Boundary Quantum Phase Transitions in the Spin Heisenberg Chain with Boundary Magnetic Fields
- Thermal effect in a causal diamond: open quantum systems approach
- Exact Boundary Modes in an Interacting Quantum Wire
- Boundary-Induced Topological and Mid-Gap States in Charge Conserving One-Dimensional Superconductors
- Free fermions with dephasing and boundary driving: Bethe Ansatz results
- The Kondo effect in the quantum spin chain