Toward a classification of PT-symmetric quantum systems: From dissipative dynamics to topology and wormholes

• URL: http://arxiv.org/abs/2311.15677v2
• Date: Mon, 13 May 2024 20:42:09 GMT
• Title: Toward a classification of PT-symmetric quantum systems: From dissipative dynamics to topology and wormholes
• Authors: Antonio M. García-García, Lucas Sá, Jacobus J. M. Verbaarschot, Can Yin,
• Abstract summary: A symmetry classification of non-Hermitian systems leads to 38 universality classes. Under certain conditions, PT-symmetric systems are grouped into 24 universality classes. Different sectors of the PT-symmetric Hamiltonian may have different symmetries.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Studies of many-body non-Hermitian parity-time (PT)-symmetric quantum systems are attracting a lot of interest due to their relevance in research areas ranging from quantum optics and continuously monitored dynamics to Euclidean wormholes in quantum gravity and dissipative quantum chaos. While a symmetry classification of non-Hermitian systems leads to 38 universality classes, we show that, under certain conditions, PT-symmetric systems are grouped into 24 universality classes. We identify 14 of them in a coupled two-site Sachdev-Ye-Kitaev (SYK) model and confirm the classification by spectral analysis using exact diagonalization techniques. Intriguingly, in 4 of these 14 universality classes, AIII$_\nu$, BDI$^\dagger_\nu$, BDI$_{++\nu}$, and CI$_{--\nu}$, we identify a basis in which the SYK Hamiltonian has a block structure in which some blocks are rectangular, with $\nu \in \mathbb{N}$ the difference between the number of rows and columns. We show analytically that this feature leads to the existence of $\nu$ robust purely \emph{real} eigenvalues, whose level statistics follow the predictions of Hermitian random matrix theory for classes A, AI, BDI, and CI, respectively. We have recently found that this $\nu$ is a topological invariant, so these classes are topological. By contrast, nontopological real eigenvalues display a crossover between Hermitian and non-Hermitian level statistics. Similarly to the case of Lindbladian dynamics, the reduction of universality classes leads to unexpected results, such as the absence of Kramers degeneracy in a given sector of the theory. Another novel feature of the classification scheme is that different sectors of the PT-symmetric Hamiltonian may have different symmetries.

Related papers

• Strong-to-weak spontaneous symmetry breaking meets average symmetry-protected topological order [17.38734393793605]
  We propose a new class of phases, termed the double ASPT phase, which emerges from a nontrivial extension of these two orders. This new phase is absent from prior studies and cannot exist in conventional closed systems.
  arXiv  Detail & Related papers  (2024-10-17T16:36:53Z)
• Quantum Chaos on Edge [36.136619420474766]
  We identify two different classes: the near edge physics of sparse'' and the near edge of dense'' chaotic systems. The distinction lies in the ratio between the number of a system's random parameters and its Hilbert space dimension. While the two families share identical spectral correlations at energy scales comparable to the level spacing, the density of states and its fluctuations near the edge are different.
  arXiv  Detail & Related papers  (2024-03-20T11:31:51Z)
• Emergent Topology in Many-Body Dissipative Quantum Matter [0.0]
  We study the dissipative dynamics of pseudo-Hermitian many-body quantum systems. We find the same topological features for a wide range of parameters suggesting that they are universal. In the limit of weak coupling to the bath, topological modes govern the approach to equilibrium.
  arXiv  Detail & Related papers  (2023-11-24T18:15:22Z)
• Homotopy, Symmetry, and Non-Hermitian Band Topology [4.777212360753631]
  We show that non-Hermitian bands exhibit intriguing exceptional points, spectral braids and crossings. We reveal different Abelian and non-Abelian phases in $mathcalPT$-symmetric systems. These results open the door for theoretical and experimental exploration of a rich variety of novel topological phenomena.
  arXiv  Detail & Related papers  (2023-09-25T18:00:01Z)
• Non-Hermitian $C_{NH} = 2$ Chern insulator protected by generalized rotational symmetry [85.36456486475119]
  A non-Hermitian system is protected by the generalized rotational symmetry $H+=UHU+$ of the system. Our finding paves the way towards novel non-Hermitian topological systems characterized by large values of topological invariants.
  arXiv  Detail & Related papers  (2021-11-24T15:50:22Z)
• Symmetry Classification and Universality in Non-Hermitian Many-Body Quantum Chaos by the Sachdev-Ye-Kitaev Model [0.0]
  For Hermitian Hamiltonians, quantum chaotic motion is related to random matrix theory spectral correlations. We show that local level statistics, which probe the dynamics around the Heisenberg time, of a non-Hermitian $q$-body Sachdev-Ye-Kitev model with $N$ Majorana fermions, are also well described by random matrix theory. We identify $19$ out of the $38$ non-Hermitian universality classes in the nHSYK model, including those corresponding to the way.
  arXiv  Detail & Related papers  (2021-10-07T13:26:17Z)
• Topological study of a Bogoliubov-de Gennes system of pseudo spin-$1/2$ bosons with conserved magnetization in a honeycomb lattice [0.0]
  We consider a non-Hermitian Hamiltonian with pseudo-Hermiticity for a system of bosons in a honeycomb lattice. Such a system is capable of acting as a topological amplifier, under time-reversal symmetry. We construct a convenient analytical description for the edge modes of the Haldane model in semi-infinite planes.
  arXiv  Detail & Related papers  (2021-10-07T02:00:12Z)
• $\PT$ Symmetry and Renormalisation in Quantum Field Theory [62.997667081978825]
  Quantum systems governed by non-Hermitian Hamiltonians with $PT$ symmetry are special in having real energy eigenvalues bounded below and unitary time evolution. We show how $PT$ symmetry may allow interpretations that evade ghosts and instabilities present in an interpretation of the theory within a Hermitian framework.
  arXiv  Detail & Related papers  (2021-03-27T09:46:36Z)
• Symmetric distinguishability as a quantum resource [21.071072991369824]
  We develop a resource theory of symmetric distinguishability, the fundamental objects of which are elementary quantum information sources. We study the resource theory for two different classes of free operations: $(i)$ $rmCPTP_A$, which consists of quantum channels acting only on $A$, and $(ii)$ conditional doubly (CDS) maps acting on $XA$.
  arXiv  Detail & Related papers  (2021-02-24T19:05:02Z)
• Boundary time crystals in collective $d$-level systems [64.76138964691705]
  Boundary time crystals are non-equilibrium phases of matter occurring in quantum systems in contact to an environment. We study BTC's in collective $d$-level systems, focusing in the cases with $d=2$, $3$ and $4$.
  arXiv  Detail & Related papers  (2021-02-05T19:00:45Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.