Quantum Geometric Tensor in $\mathcal{P}\mathcal{T}$-Symmetric Quantum Mechanics

Abstract

A series of geometric concepts are formulated for $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics and they are further unified into one entity, i.e., an extended quantum geometric tensor (QGT). The imaginary part of the extended QGT gives a Berry curvature whereas the real part induces a metric tensor on system's parameter manifold. This results in a unified conceptual framework to understand and explore physical properties of $\mathcal{P}\mathcal{T}$-symmetric systems from a geometric perspective. To illustrate the usefulness of the extended QGT, we show how its real part, i.e., the metric tensor, can be exploited as a tool to detect quantum phase transitions as well as spontaneous $\mathcal{P}\mathcal{T}$-symmetry breaking in $\mathcal{P}\mathcal{T}$-symmetric systems.

main text of 5 pages, plus supplementary material of 8 pages

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Cited by in corpus (49)

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• Quantum geometry induced second harmonic generation
• Geometric classification of non-Hermitian topological systems through the singularity ring
• General properties of fidelity in non-Hermitian quantum systems with PT symmetry
• Time-dependent $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics in generic non-Hermitian systems
• Nontrivial quantum geometry of degenerate flat bands
• Quantum metric of non-Hermitian Su-Schrieffer-Heeger systems
• Geometry and superfluidity of the flat band in a non-Hermitian optical lattice
• Generalized Quantum Geometric Tensor in a Non-Hermitian Exciton-Polariton System
• Symmetry-protected quantization of complex Berry phases in non-Hermitian many-body systems
• Visualizing quantum phase transitions in the XXZ model via the quantum steering ellipsoid
• Topological characterization of non-Hermitian multiband systems using Majorana's Stellar Representation
• Topological properties of a non-Hermitian quasi-1D chain with a flat band
• Correlation-induced coherence and its use in detecting quantum phase transitions
• Complex Berry phase and imperfect non-Hermitian phase transitions
• Super-exponential diffusion in nonlinear non-Hermitian systems
• Local geometry and quantum geometric tensor of mixed states
• Identifying non-Hermitian critical points with quantum metric
• Holonomic Gates in Pseudo-Hermitian Quantum Systems
• The effect of thermal photons on exceptional points in coupled resonators
• Quantum metric dependent anomalous velocity in systems subject to complex electric fields
• Pseudo-invariant approach for a particle in a complex time-dependent linear potential
• Formation of Exceptional Points in pseudo-Hermitian Systems
• The non-Hermitian geometrical property of 1D Lieb lattice under Majorana's stellar representation
• Sj$\ddot{\text{o}}$qvist quantum geometric tensor of finite-temperature mixed states
• Entanglement Hamiltonian and effective temperature of non-Hermitian quantum spin ladders
• A Unified View on Geometric Phases and Exceptional Points in Adiabatic Quantum Mechanics
• Quantum geometry of bosonic Bogoliubov quasiparticles
• Topological states at exceptional points
• Characterizing phase transitions and criticality in non-Hermitian extensions of the XY model
• Adiabatic Transformations in Dissipative and Non-Hermitian Phase Transitions
• Orbital anomalous Hall effect in the few-layer Weyl semimetal TaIrTe4
• Quantum geometrical effects in non-Hermitian systems
• Emerging (2+1)D electrodynamics and topological instanton in pseudo-Hermitian two-level systems
• Symmetric and Antisymmetric Tensor Products for the Function-Theoretic Operator Theorist
• Quantum geometric tensors from sub-bundle geometry
• Band topology of pseudo-Hermitian phases through tensor Berry connections and quantum metric
• Direct measurement of the quantum geometric tensor in pseudo-Hermitian systems
• Superiority of Krylov shadow tomography in estimating quantum Fisher information: From bounds to exactness
• Minimal Hamiltonian deformations as bulk probes of effective non-Hermiticity in Dirac materials
• Topological photonics in nanoscaled systems with far field radiation and polarization singularities
• Higher-order exceptional lines in a non-Hermitian JaynesCummings triangle
• Fidelity and quantum geometry approach to Dirac exceptional points in diamond nitrogen-vacancy centers
• A new Berry phase term in parity-time symmetric non-Hermitian spin-1/2 quantum systems
• Interferometric Geometric Phases of $\mathcal{P}\mathcal{T}$-symmetric Quantum Mechanics
• Covariant formulation of the Berry connection in non-Hermitian systems
• Scaling of Quantum Geometry Near the Non-Hermitian Topological Phase Transitions