Lieb-Robinson bounds, automorphic equivalence and LPPL for long-range interacting fermions

• URL: http://arxiv.org/abs/2507.03319v1
• Date: Fri, 04 Jul 2025 06:13:15 GMT
• Title: Lieb-Robinson bounds, automorphic equivalence and LPPL for long-range interacting fermions
• Authors: Stefan Teufel, Tom Wessel,
• Abstract summary: We prove a Lieb-Robinson bound for lattice fermion models with decaying interactions.<n>This allows us to prove automorphic equivalence and the local perturbations perturb locally.<n>We explain why some newer Lieb-Robinson bounds for long-range spin systems cannot be used to prove the locality of the quasi-local inverse Liouvillian.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We prove a Lieb-Robinson bound for lattice fermion models with polynomially decaying interactions, which can be used to show the locality of the quasi-local inverse Liouvillian. This allows us to prove automorphic equivalence and the local perturbations perturb locally (LPPL) principle for these systems. The proof of the Lieb-Robinson bound is based on the work of Else et al. (2020), and our results also apply to spin systems. We explain why some newer Lieb-Robinson bounds for long-range spin systems cannot be used to prove the locality of the quasi-local inverse Liouvillian, and in some cases may not even hold for fermionic systems.

Related papers

• Weak coupling limit for quantum systems with unbounded weakly commuting system operators [50.24983453990065]
  This work is devoted to a rigorous analysis of the weak coupling limit (WCL) for the reduced dynamics of an open infinite-dimensional quantum system interacting with electromagnetic field or a reservoir formed by Fermi or Bose particles.<n>We derive in the weak coupling limit the reservoir statistics, which is determined by whose terms in the multi-point correlation functions of the reservoir are non-zero in the WCL.<n>We prove that the resulting reduced system dynamics converges to unitary dynamics with a modified Hamiltonian which can be interpreted as a Lamb shift to the original Hamiltonian.
  arXiv  Detail & Related papers  (2025-05-13T05:32:34Z)
• Lindbladian reverse engineering for general non-equilibrium steady states: A scalable null-space approach [49.1574468325115]
  We introduce a method for reconstructing the corresponding Lindbaldian master equation given any target NESS. The kernel (null-space) of the correlation matrix corresponds to Lindbladian solutions. We illustrate the method in different systems, ranging from bosonic Gaussian to dissipative-driven collective spins.
  arXiv  Detail & Related papers  (2024-08-09T19:00:18Z)
• Lieb-Robinson bounds in the continuum via localized frames [0.27624021966289597]
  We study the dynamics of interacting fermions in the continuum. We first prove a Lieb-Robinson bound that is valid for a general class of local interactions. We then turn to the physical situation relevant to the (fractional) quantum Hall effect.
  arXiv  Detail & Related papers  (2024-06-21T22:03:16Z)
• On Lieb-Robinson bounds for a class of continuum fermions [0.0]
  We consider the quantum dynamics of a many-fermion system in $mathbb Rd$ with an ultraviolet regularized pair interaction. We develop a fermionic continuum notion of conditional expectation and use it to approximate time-evolved fermionic observables by local ones.
  arXiv  Detail & Related papers  (2023-10-26T18:52:30Z)
• Entanglement and localization in long-range quadratic Lindbladians [49.1574468325115]
  Signatures of localization have been observed in condensed matter and cold atomic systems. We propose a model of one-dimensional chain of non-interacting, spinless fermions coupled to a local ensemble of baths. We show that the steady state of the system undergoes a localization entanglement phase transition by tuning $p$ which remains stable in the presence of coherent hopping.
  arXiv  Detail & Related papers  (2023-03-13T12:45:25Z)
• Localization in the random XXZ quantum spin chain [55.2480439325792]
  We study the many-body localization (MBL) properties of the Heisenberg XXZ spin-$frac12$ chain in a random magnetic field. We prove that the system exhibits localization in any given energy interval at the bottom of the spectrum in a nontrivial region of the parameter space.
  arXiv  Detail & Related papers  (2022-10-26T17:25:13Z)
• Slow semiclassical dynamics of a two-dimensional Hubbard model in disorder-free potentials [77.34726150561087]
  We show that introduction of harmonic and spin-dependent linear potentials sufficiently validates fTWA for longer times. In particular, we focus on a finite two-dimensional system and show that at intermediate linear potential strength, the addition of a harmonic potential and spin dependence of the tilt, results in subdiffusive dynamics.
  arXiv  Detail & Related papers  (2022-10-03T16:51:25Z)
• Sufficient condition for gapless spin-boson Lindbladians, and its connection to dissipative time-crystals [64.76138964691705]
  We discuss a sufficient condition for gapless excitations in the Lindbladian master equation for collective spin-boson systems. We argue that gapless modes can lead to persistent dynamics in the spin observables with the possible formation of dissipative time-crystals.
  arXiv  Detail & Related papers  (2022-09-26T18:34:59Z)
• A converse to Lieb-Robinson bounds in one dimension using index theory [1.3807918535446089]
  Unitary dynamics with a strict causal cone (or "light cone") have been studied extensively, under the name of quantum cellular automata (QCAs) We show that the index theory is robust and completely extends to one-dimensional ALPUs. For the special case of finite chains with open boundaries, any unitary satisfying the Lieb-Robinson bound may be generated by such a Hamiltonian.
  arXiv  Detail & Related papers  (2020-12-01T18:59:26Z)
• Lieb-Robinson bounds imply locality of interactions [0.0]
  We show that Lieb-Robinson bounds are equivalent to the locality of the interactions. A system with k-body interactions fulfills Lieb-Robinson bounds in exponential form if and only if the interactions decay exponentially in space.
  arXiv  Detail & Related papers  (2020-06-17T18:00:03Z)
• Lieb-Robinson bounds and strongly continuous dynamics for a class of many-body fermion systems in $\mathbb{R}^d$ [0.0]
  We introduce a class of UV-regularized two-body interactions for fermions in $mathbbRd$ and prove a Lieb-Robinson estimate for the dynamics of this class of many-body systems. We also prove a propagation bound of Lieb-Robinson type for Schr"odinger operators.
  arXiv  Detail & Related papers  (2019-12-29T00:10:40Z)

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.