Many-Body Quantum Geometric Dipole

• URL: http://arxiv.org/abs/2406.12089v1
• Date: Mon, 17 Jun 2024 21:01:03 GMT
• Title: Many-Body Quantum Geometric Dipole
• Authors: H. A. Fertig, Luis Brey,
• Abstract summary: Collective excitations of many-body electron systems can carry internal structure, tied to the quantum geometry of the Hilbert space in which they are embedded. We demonstrate in this work that this property can be formulated in a generic way, which does not require wavefunctions expressed in terms of single particle-hole states. Our study demonstrates that the QGD is an intrinsic property of collective modes which is valid beyond approximations one might make for their wavefunctions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Collective excitations of many-body electron systems can carry internal structure, tied to the quantum geometry of the Hilbert space in which they are embedded. This has been shown explicitly for particle-hole-like excitations, which carry a ``quantum geometric dipole'' (QGD) that is essentially an electric dipole moment associated with the state. We demonstrate in this work that this property can be formulated in a generic way, which does not require wavefunctions expressed in terms of single particle-hole states. Our formulation exploits the density matrix associated with a branch of excitations that evolves continuously with its momentum ${\bf K}$, from which one may extract single-particle states allowing a construction of the QGD. We demonstrate the formulation using the single-mode approximation for excited states of two quantum Hall systems: the first for an integrally filled Landau level, and the second for a fractional quantum Hall state at filling factor $\nu=1/m$, with $m$ an odd integer. In both cases we obtain the same result for the QGD, which can be attributed to the translational invariance assumed of the system. Our study demonstrates that the QGD is an intrinsic property of collective modes which is valid beyond approximations one might make for their wavefunctions.

Related papers

• Quantum Entanglement in the Rabi Model with the Presence of the $A^{2}$ Term [0.0]
  The quantum Rabi model (QRM) is used to describe the light-matter interaction at the quantum level in Cavity Quantum Electrodynamics (Cavity QED) In this study, we comparatively analyze the behaviors of the QRM and the influence of the $A2$ term in the light-matter quantum Hamiltonian.
  arXiv  Detail & Related papers  (2024-09-06T18:30:32Z)
• Quantum Random Walks and Quantum Oscillator in an Infinite-Dimensional Phase Space [45.9982965995401]
  We consider quantum random walks in an infinite-dimensional phase space constructed using Weyl representation of the coordinate and momentum operators. We find conditions for their strong continuity and establish properties of their generators.
  arXiv  Detail & Related papers  (2024-06-15T17:39:32Z)
• Simulating electronic structure on bosonic quantum computers [35.884125235274865]
  One of the most promising applications of quantum computing is the simulation of many-fermion problems. We show how an electronic structure Hamiltonian can be transformed into a system of qumodes through qubit-assisted fermion-to-qumode mapping.
  arXiv  Detail & Related papers  (2024-04-16T02:04:11Z)
• A vertical gate-defined double quantum dot in a strained germanium double quantum well [48.7576911714538]
  Gate-defined quantum dots in silicon-germanium heterostructures have become a compelling platform for quantum computation and simulation. We demonstrate the operation of a gate-defined vertical double quantum dot in a strained germanium double quantum well. We discuss challenges and opportunities and outline potential applications in quantum computing and quantum simulation.
  arXiv  Detail & Related papers  (2023-05-23T13:42:36Z)
• The inflation hierarchy and the polarization hierarchy are complete for the quantum bilocal scenario [1.9798034349981157]
  We show that the quantum inflation hierarchy is complete for the bilocal scenario in the commuting observables model of locality. We also give a bilocal version of an observation by Tsirelson, namely that in finite dimensions, the commuting observables model and the tensor product model of locality coincide.
  arXiv  Detail & Related papers  (2022-12-21T19:00:09Z)
• Partition of kinetic energy and magnetic moment in dissipative diamagnetism [20.218184785285132]
  We analyze dissipative diamagnetism, arising due to dissipative cyclotron motion in two dimensions, in the light of the quantum counterpart of energy equipartition theorem. The expressions for kinetic energy and magnetic moment are reformulated in the context of superstatistics.
  arXiv  Detail & Related papers  (2022-07-30T08:07:28Z)
• Dynamical purification and the emergence of quantum state designs from the projected ensemble [0.0]
  Quantum thermalization in a many-body system is defined by the approach of local subsystems towards a universal form. Projected ensemble can mimic the behavior of a maximally entropic, uniformly random ensemble. We show that absence of dynamical purification in the space-time dual dynamics yields exact state-designs for all moments $k$ at the same time.
  arXiv  Detail & Related papers  (2022-04-28T17:19:32Z)
• Mechanism for particle fractionalization and universal edge physics in quantum Hall fluids [58.720142291102135]
  We advance a second-quantization framework that helps reveal an exact fusion mechanism for particle fractionalization in FQH fluids. We also uncover the fundamental structure behind the condensation of non-local operators characterizing topological order in the lowest-Landau-level (LLL)
  arXiv  Detail & Related papers  (2021-10-12T18:00:00Z)
• 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)
• Alternative quantisation condition for wavepacket dynamics in a hyperbolic double well [0.0]
  We propose an analytical approach for computing the eigenspectrum and corresponding eigenstates of a hyperbolic double well potential of arbitrary height or width. Considering initial wave packets of different widths and peak locations, we compute autocorrelation functions and quasiprobability distributions.
  arXiv  Detail & Related papers  (2020-09-18T10:29:04Z)
• On the evolution of quantum non-equilibrium in expanding systems [0.0]
  We study quantum ensembles in which the Born Law is initially violated (quantum non-equilibrium) We show examples of such ensembles that start close to quantum equilibrium, as measured by the standard coarse-grained H-function, but diverge from it with time.
  arXiv  Detail & Related papers  (2020-06-14T08:25:29Z)

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.