The connection between Hilbert-space return probability and real-space autocorrelations in quantum spin chains

• URL: http://arxiv.org/abs/2305.06374v1
• Date: Wed, 10 May 2023 18:00:02 GMT
• Title: The connection between Hilbert-space return probability and real-space autocorrelations in quantum spin chains
• Authors: Bikram Pain, Kritika Khanwal, and Sthitadhi Roy
• Abstract summary: We show that the temporal decay of the autocorrelation in a disordered quantum spin chain is explicitly encoded in how the return probability on Hilbert space approaches its late-time saturation. Our treatment is rooted in an understanding of the morphology of the time-evolving state on the Hilbert-space graph, and corroborated by exact numerical results.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The dynamics of interacting quantum many-body systems has two seemingly disparate but fundamental facets. The first is the dynamics of real-space local observables, and if and how they thermalise. The second is to interpret the dynamics of the many-body state as that of a fictitious particle on the underlying Hilbert-space graph. In this work, we derive an explicit connection between these two aspects of the dynamics. We show that the temporal decay of the autocorrelation in a disordered quantum spin chain is explicitly encoded in how the return probability on Hilbert space approaches its late-time saturation. As such, the latter has the same functional form in time as the decay of autocorrelations but with renormalised parameters. Our analytical treatment is rooted in an understanding of the morphology of the time-evolving state on the Hilbert-space graph, and corroborated by exact numerical results.

Related papers

• Exploring Hilbert-Space Fragmentation on a Superconducting Processor [23.39066473461786]
  Isolated interacting quantum systems generally thermalize, yet there are several counterexamples for the breakdown of ergodicity. Recently, ergodicity breaking has been observed in systems subjected to linear potentials, termed Stark many-body localization. Here, we experimentally explore initial-state dependent dynamics using a ladder-type superconducting processor with up to 24 qubits.
  arXiv  Detail & Related papers  (2024-03-14T04:39:14Z)
• Quantized Thouless pumps protected by interactions in dimerized Rydberg tweezer arrays [41.94295877935867]
  In the noninteracting case, quantized Thouless pumps can only occur when a topological singularity is encircled adiabatically. In the presence of interactions, such topological transport can even persist for exotic paths in which the system gets arbitrarily close to the noninteracting singularity.
  arXiv  Detail & Related papers  (2024-02-14T16:58:21Z)
• Real-time dynamics of false vacuum decay [49.1574468325115]
  We investigate false vacuum decay of a relativistic scalar field in the metastable minimum of an asymmetric double-well potential. We employ the non-perturbative framework of the two-particle irreducible (2PI) quantum effective action at next-to-leading order in a large-N expansion.
  arXiv  Detail & Related papers  (2023-10-06T12:44:48Z)
• Exotic quantum liquids in Bose-Hubbard models with spatially-modulated symmetries [0.0]
  We investigate the effect that spatially modulated continuous conserved quantities can have on quantum ground states. We show that such systems feature a non-trivial Hilbert space fragmentation for momenta incommensurate with the lattice. We conjecture that a Berezinskii-Kosterlitz-Thouless-type transition is driven by the unbinding of vortices along the temporal direction.
  arXiv  Detail & Related papers  (2023-07-17T18:14:54Z)
• Hilbert Space Fragmentation in Open Quantum Systems [0.7412445894287709]
  We investigate the phenomenon of Hilbert space fragmentation (HSF) in open quantum systems. We find that it can stabilize highly entangled steady states.
  arXiv  Detail & Related papers  (2023-05-05T18:00:06Z)
• Beyond semiclassical time: dynamics in quantum cosmology [0.0]
  We review two approaches to the definition of the Hilbert space and evolution in mechanical theories with local time-reparametrization invariance. We discuss in which sense both approaches exhibit an inner product that is gauge-fixed via an operator version of the usual Faddeev-Popov procedure. We note that a conditional probability interpretation of the physical states is possible, so that both formalisms are examples of quantum mechanics with a relational dynamics.
  arXiv  Detail & Related papers  (2023-02-15T19:00:09Z)
• Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum [77.34726150561087]
  We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians. We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
  arXiv  Detail & Related papers  (2023-01-18T09:26:02Z)
• Particle mixing and the emergence of classicality: A spontaneous-collapse-model view [0.0]
  We show that spontaneous collapse can induce the decay dynamics in both quantum state and master equations. We show that the decay property of a flavor-oscillating system is intimately connected to the time (a)symmetry of the noise field underlying the collapse mechanism.
  arXiv  Detail & Related papers  (2020-08-25T16:07:59Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)
• Exploring 2D synthetic quantum Hall physics with a quasi-periodically driven qubit [58.720142291102135]
  Quasi-periodically driven quantum systems are predicted to exhibit quantized topological properties. We experimentally study a synthetic quantum Hall effect with a two-tone drive.
  arXiv  Detail & Related papers  (2020-04-07T15:00:41Z)
• Many-Body Dephasing in a Trapped-Ion Quantum Simulator [0.0]
  How a closed interacting quantum many-body system relaxes and dephases as a function of time is a fundamental question in thermodynamic and statistical physics. We analyse and observe the persistent temporal fluctuations after a quantum quench of a tunable long-range interacting transverse-field Ising Hamiltonian realized with a trapped-ion quantum simulator.
  arXiv  Detail & Related papers  (2020-01-08T12:33:28Z)

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.