Complexity enriched dynamical phases for fermions on graphs

• URL: http://arxiv.org/abs/2404.08055v2
• Date: Mon, 14 Oct 2024 05:12:15 GMT
• Title: Complexity enriched dynamical phases for fermions on graphs
• Authors: Wei Xia, Jie Zou, Xiaopeng Li,
• Abstract summary: We investigate entanglement and Krylov complexity for fermions on regular graphs. Our investigations unveil that while entanglement follows volume laws on both types of regular graphs with degree $d = 2$ and $d = 3$, the Krylov complexity exhibits distinctive behaviors. For interacting fermions, our theoretical analyses find the dimension scales as $Dsim 4Nalpha$ for regular graphs of $d = 2$ with $0.38leqalphaleq0.59$, whereas it scales as $Dsim 4N$ for $d = 3$.
• Score: 17.70942538295701
• License:
• Abstract: Dynamical quantum phase transitions, encompassing phenomena like many-body localization transitions and measurement-induced phase transitions, are often characterized and identified through the analysis of quantum entanglement. Here, we highlight that the dynamical phases defined by entanglement are further enriched by complexity. We investigate both the entanglement and Krylov complexity for fermions on regular graphs, which can be implemented by systems like $^6$Li atoms confined by optical tweezers. Our investigations unveil that while entanglement follows volume laws on both types of regular graphs with degree $d = 2$ and $d = 3$, the Krylov complexity exhibits distinctive behaviors. We analyze both free fermions and interacting fermions models. In the absence of interaction, both numerical results and theoretical analysis confirm that the dimension of the Krylov space scales as $D\sim N$ for regular graphs of degree $d = 2$ with $N$ sites, and we have $D\sim N^2$ for $d = 3$. The qualitative distinction also persists in interacting fermions on regular graphs. For interacting fermions, our theoretical analyses find the dimension scales as $D\sim 4^{N^\alpha}$ for regular graphs of $d = 2$ with $0.38\leq\alpha\leq0.59$, whereas it scales as $D\sim 4^N$ for $d = 3$. The distinction in the complexity of quantum dynamics for fermions on graphs with different connectivity can be probed in experiments by measuring the out-of-time-order correlators.

Related papers

• Entanglement Transition due to particle losses in a monitored fermionic chain [0.0]
  We study the dynamics of the entanglement entropy under quantum jumps that induce local particle losses in a model of free fermions hopping. We show that by tuning the system parameters, a measurement-induced entanglement transition occurs where the entanglement entropy scaling changes from logarithmic to area-law.
  arXiv  Detail & Related papers  (2024-08-07T11:30:09Z)
• 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)
• KPZ scaling from the Krylov space [83.88591755871734]
  Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang scaling in late-time correlators and autocorrelators has been reported. Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis.
  arXiv  Detail & Related papers  (2024-06-04T20:57:59Z)
• $\mathbb{Z}_N$ lattice gauge theories with matter fields [0.0]
  We study fermions and bosons in $mathbb Z_N$ lattice gauge theories. We present analytical arguments for the most important phases and estimates for phase boundaries of the model.
  arXiv  Detail & Related papers  (2023-08-24T21:05:15Z)
• 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)
• Studying chirality imbalance with quantum algorithms [62.997667081978825]
  We employ the (1+1) dimensional Nambu-Jona-Lasinio (NJL) model to study the chiral phase structure and chirality charge density of strongly interacting matter. By performing the Quantum imaginary time evolution (QITE) algorithm, we simulate the (1+1) dimensional NJL model on the lattice at various temperature $T$ and chemical potentials $mu$, $mu_5$.
  arXiv  Detail & Related papers  (2022-10-06T17:12:33Z)
• Decoherent Quench Dynamics across Quantum Phase Transitions [0.0]
  We formulate decoherent dynamics induced by continuous quantum non-demolition measurements of the instantaneous Hamiltonian. We generalize the well-studied universal Kibble-Zurek behavior for linear temporal drive across the critical point. We show that the freeze-out time scale can be probed from the relaxation of the Hall conductivity.
  arXiv  Detail & Related papers  (2021-03-14T23:43:55Z)
• Quantum aspects of chaos and complexity from bouncing cosmology: A study with two-mode single field squeezed state formalism [0.0]
  This paper is devoted to the study of out-of-equilibrium aspects and quantum chaos appearing in the universe. We use the $Out-of-Time Ordered correlation (OTOC)$ functions for probing the random behaviour of the universe both at early and the late times.
  arXiv  Detail & Related papers  (2020-09-08T16:10:52Z)
• On the four-body problem in the Born-Oppenheimer approximation [0.0]
  The model allows exact solvability and a critical analysis of the Born-Oppenheimer approximation. It is shown that the sum of the first two terms of the Puiseux series, in powers of the dimensionless parameter $sigma=fracmM$, coincide exactly with the values obtained in the Born-Oppenheimer approximation.
  arXiv  Detail & Related papers  (2020-07-29T16:43:03Z)
• Continuous-time quantum walks in the presence of a quadratic perturbation [55.41644538483948]
  We address the properties of continuous-time quantum walks with Hamiltonians of the form $mathcalH= L + lambda L2$. We consider cycle, complete, and star graphs because paradigmatic models with low/high connectivity and/or symmetry.
  arXiv  Detail & Related papers  (2020-05-13T14:53:36Z)
• 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.