Breakdown of Fermi's Golden Rule in 1d systems at non-zero temperature

• URL: http://arxiv.org/abs/2508.00254v1
• Date: Fri, 01 Aug 2025 01:51:50 GMT
• Title: Breakdown of Fermi's Golden Rule in 1d systems at non-zero temperature
• Authors: Thomas Young, Jerome LLoyd, Curt von Keyserlingk,
• Abstract summary: In interacting quantum systems, the single-particle Green's function is expected to decay in time due to the interaction induced decoherence of quasiparticles.<n>We argue that this effect is present in a wide variety of well-known weakly interacting quantum fermionic and bosonic systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In interacting quantum systems, the single-particle Green's function is expected to decay in time due to the interaction induced decoherence of quasiparticles. In the limit of weak interaction strengths ($\Delta$), a naive application of Fermi's Golden Rule (FGR) predicts an $\mathcal{O}(\Delta^{2})$ quasiparticle decay rate. However, for 1d fermions on the lattice at $T>0$, this calculation gives a divergent result and the scaling of the quasiparticle lifetime with interaction strength remains an open question. In this work we propose a solution to this question: combining numerical simulations using the recently introduced dissipation-assisted operator evolution (DAOE) method, with non-perturbative diagrammatic re-summations, we predict a logarithmic enhancement of the quasiparticle decay rate $\tau^{-1} \sim \Delta^{2} \log \Delta^{-2}$. We argue that this effect is present in a wide variety of well-known weakly interacting quantum fermionic and bosonic systems, and even in some classical systems, provided the non-interacting limit has quasiparticles with a generic dispersion.

Related papers

• Universal Bound States in Long-range Spin Chains with an Impurity [11.213906010203264]
  We show that distinct classes of universal three-magnon states can emerge when the impurity-mediated two-magnon interaction is on resonance.<n>Our results could be tested experimentally in the future on quantum simulation platforms.
  arXiv  Detail & Related papers  (2025-07-07T13:31:45Z)
• 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)
• Polynomial Time Quantum Gibbs Sampling for Fermi-Hubbard Model at any Temperature [9.62464358196899]
  We prove a constant gap of the perturbed Lindbladian corresponding to interacting fermions up to some maximal coupling strength.<n>This is achieved by using theorems about stability of the gap for lattice fermions.<n>As an application, we explain how to calculate partition functions for the considered systems.
  arXiv  Detail & Related papers  (2025-01-02T18:56:02Z)
• Hamiltonians for Quantum Systems with Contact Interactions [49.1574468325115]
  We show that in the limit one obtains the one-body Hamiltonian for the light particle subject to $N$ (non-local) point interactions placed at fixed positions. We will verify that such non-local point interactions do not exhibit the ultraviolet pathologies that are present in the case of standard local point interactions.
  arXiv  Detail & Related papers  (2024-07-09T14:04:11Z)
• Clustering theorem in 1D long-range interacting systems at arbitrary temperatures [0.0]
  This paper delves into a fundamental aspect of quantum statistical mechanics -- the absence of thermal phase transitions in one-dimensional (1D) systems.<n>We successfully derive a clustering theorem applicable to a wide range of interaction decays at arbitrary temperatures.<n>Our findings indicate the absence of phase transitions in 1D systems with super-polynomially decaying interactions.
  arXiv  Detail & Related papers  (2024-03-18T02:54:55Z)
• The ballistic to diffusive crossover in a weakly-interacting Fermi gas [0.0]
  We develop a numerical method to simulate systems of fermions at high temperatures by adapting Dissipation-assisted Operator Evolution to fermions. Applying our method to a microscopic model of weakly interacting fermions, we numerically demonstrate that the crossover from ballistic to diffusive transport happens at a time. We substantiate this scaling with a Fermi's golden rule calculation in the operator spreading picture, interpreting $t_D$ as the fermion-fermion scattering time and lifetime of the single-particle Green's function.
  arXiv  Detail & Related papers  (2023-10-24T17:57:11Z)
• Theory of free fermions under random projective measurements [43.04146484262759]
  We develop an analytical approach to the study of one-dimensional free fermions subject to random projective measurements of local site occupation numbers. We derive a non-linear sigma model (NLSM) as an effective field theory of the problem.
  arXiv  Detail & Related papers  (2023-04-06T15:19:33Z)
• Formation of robust bound states of interacting microwave photons [148.37607455646454]
  One of the hallmarks of interacting systems is the formation of multi-particle bound states. We develop a high fidelity parameterizable fSim gate that implements the periodic quantum circuit of the spin-1/2 XXZ model. By placing microwave photons in adjacent qubit sites, we study the propagation of these excitations and observe their bound nature for up to 5 photons.
  arXiv  Detail & Related papers  (2022-06-10T17:52:29Z)
• In-Gap Band Formation in a Periodically Driven Charge Density Wave Insulator [68.8204255655161]
  Periodically driven quantum many-body systems host unconventional behavior not realized at equilibrium. We investigate such a setup for strongly interacting spinless fermions on a chain, which at zero temperature and strong interactions form a charge density wave insulator.
  arXiv  Detail & Related papers  (2022-05-19T13:28:47Z)
• Analyticity constraints bound the decay of the spectral form factor [0.0]
  Quantum chaos cannot develop faster than $lambda leq 2 pi/(hbar beta)$ for systems in thermal equilibrium. We show that similar constraints also bound the decay of the spectral form factor (SFF) The relation of the derived bound with other known bounds, including quantum speed limits, is discussed.
  arXiv  Detail & Related papers  (2022-02-23T19:00:00Z)
• Fast Thermalization from the Eigenstate Thermalization Hypothesis [69.68937033275746]
  Eigenstate Thermalization Hypothesis (ETH) has played a major role in understanding thermodynamic phenomena in closed quantum systems. This paper establishes a rigorous link between ETH and fast thermalization to the global Gibbs state. Our results explain finite-time thermalization in chaotic open quantum systems.
  arXiv  Detail & Related papers  (2021-12-14T18:48:31Z)
• Effective Theory for the Measurement-Induced Phase Transition of Dirac Fermions [0.0]
  A wave function exposed to measurements undergoes pure state dynamics. For many-particle systems, the competition of these different elements of dynamics can give rise to a scenario similar to quantum phase transitions. A key finding is that this field theory decouples into one set of degrees of freedom that heats up indefinitely.
  arXiv  Detail & Related papers  (2021-02-16T19:00:00Z)
• Evolution of a Non-Hermitian Quantum Single-Molecule Junction at Constant Temperature [62.997667081978825]
  We present a theory for describing non-Hermitian quantum systems embedded in constant-temperature environments. We find that the combined action of probability losses and thermal fluctuations assists quantum transport through the molecular junction.
  arXiv  Detail & Related papers  (2021-01-21T14:33:34Z)
• Mesoscopic quantum superposition states of weakly-coupled matter-wave solitons [58.720142291102135]
  We establish quantum features of an atomic soliton Josephson junction (SJJ) device. We show that the SJJ-model in quantum domain exhibits unusual features due to its effective nonlinear strength proportional to the square of total particle number. We have shown that the obtained quantum state is more resistant to few particle losses from the condensates if tiny components of entangled Fock states are present.
  arXiv  Detail & Related papers  (2020-11-26T09:26:19Z)

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.