The Anthony J Leggett Institute for Condensed Matter Special Theory Seminar - "Non-Hermitian analogue gravity" (Diego Felipe Munoz-Arboleda, Utrecht University)

Non-Hermitian systems have emerged as a versatile platform for exploring novel topological phases, unconventional critical phenomena, and open quantum dynamics beyond the framework of Hermitian quantum mechanics. In this talk, I will present our recent work on the interplay between non-Hermitian topology, thermodynamics, and analogue gravity in one-dimensional lattice models with gain/loss and non-reciprocal hopping.

I  will first discuss how thermodynamic and entanglement properties reveal the nature of topological phase transitions in non-Hermitian systems [1]. In particular, the heat capacity reproduces the expected conformal scaling for Dirac critical points, while transitions associated with complex-energy phases exhibit an unconventional critical behavior connected to the emergence of an imaginary time crystal.

The main part of the talk will focus on a non-Hermitian tight-binding model that realizes an analogue black hole [2]. A spatial modulation of the non-reciprocal hopping generates an effective Painlevé–Gullstrand spacetime with analogue event horizons, allowing the extraction of Hawking temperatures, analogue black-hole entropy, and emission spectra directly from the lattice model. I will then show how this framework naturally extends to open quantum systems through a Lindblad description, where the effective non-Hermitian Hamiltonian captures the single-particle physics while the full open-system dynamics reveal horizon signatures in the steady state.

Finally, I will present our recent progress toward identifying genuinely many-body signatures of analogue Hawking radiation using bosonic Gaussian methods [3], including non-local density-density correlations and anomalous Hawking-partner correlations. These results illustrate how non-Hermitian systems provide a unified framework connecting topology, quantum thermodynamics, open quantum dynamics, and emergent gravitational phenomena.

References:

[1] https://journals.aps.org/prb/abstract/10.1103/PhysRevB.110.115135

[2] https://journals.aps.org/prb/abstract/10.1103/vdsx-r3dq

[3] In preparation