Symmetry-enhanced Lieb-Robinson bounds for a class of Bose-Hubbard type Hamiltonians

• URL: http://arxiv.org/abs/2405.04672v2
• Date: Tue, 08 Jul 2025 21:31:25 GMT
• Title: Symmetry-enhanced Lieb-Robinson bounds for a class of Bose-Hubbard type Hamiltonians
• Authors: Tomotaka Kuwahara, Marius Lemm,
• Abstract summary: We show that translation invariance combined with local $p$-body repulsion alters the propagation behavior.<n>Our result identifies symmetry-driven constraints as a new mechanism for suppressing propagation speed in bosonic systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Several recent works have derived Lieb-Robinson bounds (LRBs) for Bose-Hubbard-type Hamiltonians. For certain structured initial states, e.g., vacuum perturbations or near-stationary states, information propagates with velocity $v \leq C$ . However, for general bounded-density initial states, it was shown by the first author, Vu, and Saito that the velocity can grow in time as $v \sim t^{D-1}$, where $D$ is the spatial dimension -- demonstrating the possibility of accelerated information spreading in bosonic systems. In this work, we introduce a new perspective on this phenomenon: we show that translation invariance combined with local $p$-body repulsion ($n^p$ with $p > D+1$) qualitatively alters the propagation behavior, leading to a bound of the form $v \sim t^{\frac{D}{p - D - 1}}$ for general bounded-energy-density initial states. In particular, this establishes for an almost-linear light cone at large $p$, in stark contrast to the previously found accelerated regimes. Our result identifies symmetry-driven constraints as a new mechanism for suppressing propagation speed in bosonic systems and thereby reframes the scope of what types of LRBs can hold. We further provide matching examples showing that, under the given assumptions, this bound is sharp -- no further improvement in the power of $t$ is possible without invoking additional dynamical constraints.

Related papers

• Approximation of diffeomorphisms for quantum state transfers [49.1574468325115]
  We seek to combine two emerging standpoints in control theory.<n>We numerically find control laws driving state transitions in small time in a bilinear Schr"odinger PDE posed on the torus.
  arXiv  Detail & Related papers  (2025-03-18T17:28:59Z)
• Lieb-Robinson bounds with exponential-in-volume tails [0.0]
  Lieb-Robinson bounds demonstrate the emergence of locality in many-body quantum systems. Perturbation theory and cluster expansion methods suggest that at short times, volume-filling operators are suppressed. We show that disorder operators have volume-law suppression near the "solvable (Ising) point" in quantum phases with spontaneous symmetry breaking.
  arXiv  Detail & Related papers  (2025-02-04T19:00:12Z)
• From spin squeezing to fast state discrimination [0.0]
  A class of entangled states are spin-squeezed states of $N$ two-level atoms. We show that atomic interactions generate a nonlinear evolution that shears the state's probability density. The resulting nonlinearity is known to be a powerful resource in quantum computation.
  arXiv  Detail & Related papers  (2024-10-29T13:30:29Z)
• Non-asymptotic bounds for forward processes in denoising diffusions: Ornstein-Uhlenbeck is hard to beat [49.1574468325115]
  This paper presents explicit non-asymptotic bounds on the forward diffusion error in total variation (TV) We parametrise multi-modal data distributions in terms of the distance $R$ to their furthest modes and consider forward diffusions with additive and multiplicative noise.
  arXiv  Detail & Related papers  (2024-08-25T10:28:31Z)
• Geometry of degenerate quantum states, configurations of $m$-planes and invariants on complex Grassmannians [55.2480439325792]
  We show how to reduce the geometry of degenerate states to the non-abelian connection $A$. We find independent invariants associated with each triple of subspaces. Some of them generalize the Berry-Pancharatnam phase, and some do not have analogues for 1-dimensional subspaces.
  arXiv  Detail & Related papers  (2024-04-04T06:39:28Z)
• Bound-state confinement after trap-expansion dynamics in integrable systems [0.0]
  We investigate bound-state transport in the spin-$1/2$ anisotropic Heisenberg chain ($XXZ$ chain) In the hydrodynamic regime, if interactions are strong enough, bound states remain confined in the initial region. Fingerprints of confinement are visible in the space-time profiles of local spin-projection operators.
  arXiv  Detail & Related papers  (2024-02-27T15:50:19Z)
• Small-time controllability for the nonlinear Schr\"odinger equation on $\mathbb{R}^N$ via bilinear electromagnetic fields [55.2480439325792]
  We address the small-time controllability problem for a nonlinear Schr"odinger equation (NLS) on $mathbbRN$ in the presence of magnetic and electric external fields. In detail, we study when it is possible to control the dynamics of (NLS) as fast as desired via sufficiently large control signals.
  arXiv  Detail & Related papers  (2023-07-28T21:30:44Z)
• Radial power-like potentials: from the Bohr-Sommerfeld $S$-state energies to the exact ones [0.0]
  The Bohr-Sommerfeld (B-S) quantization condition for $S$-states of the $d$-dimensional radial Schr"odinger equation is proposed.
  arXiv  Detail & Related papers  (2023-05-19T00:51:02Z)
• Infinite bound states and $1/n$ energy spectrum induced by a Coulomb-like potential of type III in a flat band system [0.0]
  We investigate the bound states in a one-dimensional spin-1 flat band system with a Coulomb-like potential of type III. Near the threshold of continuous spectrum, the bound state energy is consistent with the ordinary hydrogen-like atom energy level formula.
  arXiv  Detail & Related papers  (2022-05-21T01:09:04Z)
• Power-like potentials: from the Bohr-Sommerfeld energies to exact ones [77.34726150561087]
  Bohr-Sommerfeld Energies (BSE) extracted explicitly from the Bohr-Sommerfeld quantization condition are compared with the exact energies. For physically important cases $m=1,4,6$ for the $100$th excited state BSE coincide with exact ones in 5-6 figures.
  arXiv  Detail & Related papers  (2021-07-31T21:37:50Z)
• Finite speed of quantum information in models of interacting bosons at finite density [0.22843885788439797]
  We prove that quantum information propagates with a finite velocity in any model of interacting bosons whose Hamiltonian contains spatially local single-boson hopping terms. Our bounds are relevant for physically realistic initial conditions in experimentally realized models of interacting bosons.
  arXiv  Detail & Related papers  (2021-06-17T18:00:00Z)
• Double-trace deformation in Keldysh field theory [0.0]
  We introduce a general Keldysh action that maximally obeys Weinbergian constraints. We find that driven-dissipative dynamics is much richer than thermodynamics.
  arXiv  Detail & Related papers  (2020-12-10T00:16:47Z)
• Anharmonic oscillator: a solution [77.34726150561087]
  The dynamics in $x$-space and in $(gx)-space corresponds to the same energy spectrum with effective coupling constant $hbar g2$. A 2-classical generalization leads to a uniform approximation of the wavefunction in $x$-space with unprecedented accuracy.
  arXiv  Detail & Related papers  (2020-11-29T22:13:08Z)
• Scattering data and bound states of a squeezed double-layer structure [77.34726150561087]
  A structure composed of two parallel homogeneous layers is studied in the limit as their widths $l_j$ and $l_j$, and the distance between them $r$ shrinks to zero simultaneously. The existence of non-trivial bound states is proven in the squeezing limit, including the particular example of the squeezed potential in the form of the derivative of Dirac's delta function. The scenario how a single bound state survives in the squeezed system from a finite number of bound states in the finite system is described in detail.
  arXiv  Detail & Related papers  (2020-11-23T14:40:27Z)
• Quasiparticle dynamics of symmetry resolved entanglement after a quench: the examples of conformal field theories and free fermions [0.0]
  We show how the entanglement splits between the sectors of an internal local symmetry of a quantum many-body system. We point out two physically relevant effects that should be easily observed in atomic experiments.
  arXiv  Detail & Related papers  (2020-10-19T19:12:42Z)
• Sub-bosonic (deformed) ladder operators [62.997667081978825]
  We present a class of deformed creation and annihilation operators that originates from a rigorous notion of fuzziness. This leads to deformed, sub-bosonic commutation relations inducing a simple algebraic structure with modified eigenenergies and Fock states. In addition, we investigate possible consequences of the introduced formalism in quantum field theories, as for instance, deviations from linearity in the dispersion relation for free quasibosons.
  arXiv  Detail & Related papers  (2020-09-10T20:53:58Z)
• Perturbation theory near degenerate exceptional points [0.0]
  The Hamiltonians $H=H_0+lambda V$ are non-Hermitian and lie close to their unobservable exceptional-point (EP) degeneracy limit. The method of construction of the bound states is described. The emergence of a counterintuitive connection between the value of $L$, the structure of the matrix elements of perturbations, and the possible loss of the stability and unitarity of the processes of the unfolding of the EP is given a detailed explanation.
  arXiv  Detail & Related papers  (2020-08-02T13:28:00Z)
• 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.