$\mathcal{P}\mathcal{T}$-symmetric, non-Hermitian quantum many-body physics -- a methodological perspective

Abstract

We review the methodology to theoretically treat parity-time- ($\mathcal{P}\mathcal{T}$-) symmetric, non-Hermitian quantum many-body systems... (For the full abstract see paper)

56 pages, 12 figures. Published version with updated references

References in corpus (18)

• Making Sense of Non-Hermitian Hamiltonians
• The physics of exceptional points
• Quantum trajectories and open many-body quantum systems
• Observation of parity-time symmetry breaking in a single spin system
• New topological invariants in non-Hermitian systems
• The Naimark dilated PT-symmetric brachistochrone
• Mixed-state evolution in the presence of gain and loss
• An Equivalent Hermitian Hamiltonian for the non-Hermitian -x^4 Potential
• Equivalence of a Complex $\cP\cT$-Symmetric Quartic Hamiltonian and a Hermitian Quartic Hamiltonian with an Anomaly
• Impurity and correlation effects on transport in one-dimensional quantum wires
• Universal properties of dissipative Tomonaga-Luttinger liquids: Case study of a non-Hermitian XXZ spin chain
• Theory of superconductivity with non-Hermitian and parity-time reversal symmetric cooper pairing symmetry
• Conventional quantum phase transition driven by complex parameter in non-Hermitian PT-symmetric Ising model
• Correlations at PT-symmetric quantum critical point
• The disappearing $Q$ operator
• On the Path-Integral Derivation of the Anomaly for the Hermitian Equivalent of the Complex $PT$-Symmetric Quartic Hamiltonian
• Path-Integral Formulation of Pseudo-Hermitian Quantum Mechanics and the Role of the Metric Operator
• Signature of PT-symmetric non-Hermitian superconductivity in angle-resolved photoelectron fluctuation spectroscopy

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• Correlations and Krylov spread for a non-Hermitian Hamiltonian: Ising chain with a complex-valued transverse magnetic field
• Correlation versus dissipation in a non-Hermitian Anderson impurity model
• Phase transitions in a non-Hermitian Su-Schrieffer-Heeger model via Krylov spread complexity
• Phase diagram of non-Hermitian BCS superfluids in a dissipative asymmetric Hubbard model
• Formal Green's function theory in non-Hermitian lattice systems
• Three perspectives on entropy dynamics in a non-Hermitian two-state system
• Work statistics and generalized Loschmidt echo for the Hatano-Nelson model
• Vacuum Rabi Splitting and Quantum Fisher Information of a Non-Hermitian Qubit in a Single-Mode Cavity
• Breakdown of Linear Spin-Wave Theory in a Non-Hermitian Quantum Spin Chain
• Quantum implementation of non-unitary operations with biorthogonal representations
• Meissner effect in non-Hermitian superconductors
• Disorder and non-Hermiticity in Kitaev spin liquids with a Majorana Fermi surface
• Edge states and persistent current in a PT-symmetric extended Su-Schrieffer-Heeger model with generic boundary conditions
• Physical constraints on effective non-Hermitian systems
• Quantifying non-Hermiticity using single- and many-particle quantum properties
• Probing phase transitions in non-Hermitian systems with quantum entanglement
• Fidelity and quantum geometry approach to Dirac exceptional points in diamond nitrogen-vacancy centers