Response theory for locally gapped systems

• URL: http://arxiv.org/abs/2410.10809v1
• Date: Mon, 14 Oct 2024 17:59:29 GMT
• Title: Response theory for locally gapped systems
• Authors: Joscha Henheik, Tom Wessel,
• Abstract summary: We introduce a notion of a emphlocal gap for interacting many-body quantum lattice systems. We prove the validity of response theory and Kubo's formula for localized perturbations in such settings.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce a notion of a \emph{local gap} for interacting many-body quantum lattice systems and prove the validity of response theory and Kubo's formula for localized perturbations in such settings. On a high level, our result shows that the usual spectral gap condition, concerning the system as a whole, is not a necessary condition for understanding local properties of the system. More precisely, we say that an equilibrium state $\rho_0$ of a Hamiltonian $H_0$ is locally gapped in $\Lambda^{\mathrm{gap}} \subset \Lambda$, whenever the Liouvillian $- \mathrm{i} \, [H_0, \, \cdot \, ]$ is almost invertible on local observables supported in $\Lambda^{\mathrm{gap}}$ when tested in $\rho_0$. To put this into context, we provide other alternative notions of a local gap and discuss their relations. The validity of response theory is based on the construction of \emph{non-equilibrium almost stationary states} (NEASSs). By controlling locality properties of the NEASS construction, we show that response theory holds to any order, whenever the perturbation \(\epsilon V\) acts in a region which is further than $|\log \epsilon|$ away from the non-gapped region $\Lambda \setminus \Lambda^{\mathrm{gap}}$.

Related papers

• Extracting Dynamical Maps of Non-Markovian Open Quantum Systems [0.0]
  We show thatLambda(tau)$ arises from suddenly coupling a system to one or more thermal baths with a strength that is neither weak nor strong. We employ the Choi-Jamiolkowski isomorphism so that $hatLambda(tau)$ can be fully reconstructed. Our numerical examples of interacting spinless Fermi chains and the single impurity Anderson model demonstrate regimes where our approach can offer a significant speedup.
  arXiv  Detail & Related papers  (2024-09-25T16:09:03Z)
• On stability of k-local quantum phases of matter [0.4999814847776097]
  We analyze the stability of the energy gap to Euclids for Hamiltonians corresponding to general quantum low-density parity-check codes. We discuss implications for the third law of thermodynamics, as $k$-local Hamiltonians can have extensive zero-temperature entropy.
  arXiv  Detail & Related papers  (2024-05-29T18:00:20Z)
• Dimension Independent Disentanglers from Unentanglement and Applications [55.86191108738564]
  We construct a dimension-independent k-partite disentangler (like) channel from bipartite unentangled input. We show that to capture NEXP, it suffices to have unentangled proofs of the form $| psi rangle = sqrta | sqrt1-a | psi_+ rangle where $| psi_+ rangle has non-negative amplitudes.
  arXiv  Detail & Related papers  (2024-02-23T12:22:03Z)
• Constructions of $k$-uniform states in heterogeneous systems [65.63939256159891]
  We present two general methods to construct $k$-uniform states in the heterogeneous systems for general $k$. We can produce many new $k$-uniform states such that the local dimension of each subsystem can be a prime power.
  arXiv  Detail & Related papers  (2023-05-22T06:58:16Z)
• Nonlocality under Computational Assumptions [51.020610614131186]
  A set of correlations is said to be nonlocal if it cannot be reproduced by spacelike-separated parties sharing randomness and performing local operations. We show that there exist (efficient) local producing measurements that cannot be reproduced through randomness and quantum-time computation.
  arXiv  Detail & Related papers  (2023-03-03T16:53:30Z)
• Prethermalization and the local robustness of gapped systems [0.22843885788439797]
  We prove that prethermalization is a generic property of gapped local many-body quantum systems. We infer the robustness of quantum simulation in low-energy subspaces.
  arXiv  Detail & Related papers  (2022-09-22T18:00:01Z)
• Random quantum circuits transform local noise into global white noise [118.18170052022323]
  We study the distribution over measurement outcomes of noisy random quantum circuits in the low-fidelity regime. For local noise that is sufficiently weak and unital, correlations (measured by the linear cross-entropy benchmark) between the output distribution $p_textnoisy$ of a generic noisy circuit instance shrink exponentially. If the noise is incoherent, the output distribution approaches the uniform distribution $p_textunif$ at precisely the same rate.
  arXiv  Detail & Related papers  (2021-11-29T19:26:28Z)
• Maximal gap between local and global distinguishability of bipartite quantum states [7.605814048051737]
  We prove a tight and close-to-optimal lower bound on the effectiveness of local quantum measurements (without classical communication) at discriminating any two bipartite quantum states.
  arXiv  Detail & Related papers  (2021-10-08T21:40:02Z)
• Threshold Phenomena in Learning Halfspaces with Massart Noise [56.01192577666607]
  We study the problem of PAC learning halfspaces on $mathbbRd$ with Massart noise under Gaussian marginals. Our results qualitatively characterize the complexity of learning halfspaces in the Massart model.
  arXiv  Detail & Related papers  (2021-08-19T16:16:48Z)
• The distribution of localization measures of chaotic eigenstates in the stadium billiard [0.0]
  The localization measures $A$ of localized chaotic eigenstates in the Poincar'e-Husimi representation. The dependence of the standard deviation $sigma$ on $alpha$ is analyzed, as well as on the spectral parameter $beta$.
  arXiv  Detail & Related papers  (2021-04-18T17:30:06Z)
• Anisotropy-mediated reentrant localization [62.997667081978825]
  We consider a 2d dipolar system, $d=2$, with the generalized dipole-dipole interaction $sim r-a$, and the power $a$ controlled experimentally in trapped-ion or Rydberg-atom systems. We show that the spatially homogeneous tilt $beta$ of the dipoles giving rise to the anisotropic dipole exchange leads to the non-trivial reentrant localization beyond the locator expansion.
  arXiv  Detail & Related papers  (2020-01-31T19:00:01Z)

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.