Quantum Spin Systems
- URL: http://arxiv.org/abs/2308.07848v1
- Date: Tue, 15 Aug 2023 15:52:55 GMT
- Title: Quantum Spin Systems
- Authors: Amanda Young
- Abstract summary: This work provides an overview of gapped quantum spin systems, including concepts, techniques, properties, and results.
The basic framework and objects of interest for quantum spin systems are introduced, and the main ideas behind methods for proving spectral gaps for frustration-free models are outlined.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: This work provides an overview of gapped quantum spin systems, including
concepts, techniques, properties, and results. The basic framework and objects
of interest for quantum spin systems are introduced, and the main ideas behind
methods for proving spectral gaps for frustration-free models are outlined.
After reviewing recent progress on several spectral gap conjectures, we discuss
quasi-locality of the Heisenberg dynamics and its utility in proving properties
of gapped quantum spin systems. Lieb-Robinson bounds have played a central role
in establishing exponential decay of ground state correlations, an area law for
one-dimensional systems, a many-body adiabatic theorem, and spectral gap
stability. They also aided in the development of the quasi-adiabatic
continuation, which is a useful for investigating gapped ground state phases,
both of which are also discussed.
Related papers
- Phase space geometry of collective spin systems: Scaling and Fractality [0.0]
We examine the scaling of the inverse participation ratio of spin coherent states in the energy basis of three collective spin systems.
For the Quantum Kicked Top, the fractal dimension of coherent states -- when well-defined -- exhibits three general behaviors.
arXiv Detail & Related papers (2025-02-21T03:11:52Z) - Exploring nontrivial topology at quantum criticality in a superconducting processor [23.278631632470628]
We present an experimental exploration of the critical cluster Ising model by preparing its low-lying critical states on a superconducting processor with up to $100$ qubits.
We develop an efficient method to probe the boundary $g$-function based on prepared low-energy states, which allows us to uniquely identify the nontrivial topology of the critical systems under study.
Our results demonstrate the low-lying critical states as useful quantum resources for investigating the interplay between topology and quantum criticality.
arXiv Detail & Related papers (2025-01-08T18:39:44Z) - Observation of quantum superposition of topological defects in a trapped ion quantum simulator [10.307677845109378]
We report the observation of quantum superposition of topological defects in a trapped-ion quantum simulator.
Our work provides useful tools for non-equilibrium dynamics in quantum Kibble-Zurek physics.
arXiv Detail & Related papers (2024-10-20T13:27:13Z) - From angular coefficients to quantum observables: a phenomenological appraisal in di-boson systems [44.99833362998488]
Motivated by the growing interest in accessing the spin structure of multi-boson processes, we study polarisation and spin-correlation coefficients in di-boson systems.
We show that higher-order corrections of QCD and electroweak type, off-shell modelling, and realistic effects such as fiducial selections and neutrino reconstruction are unavoidable.
arXiv Detail & Related papers (2024-09-25T08:30:54Z) - Dephasing in the central spin problem with long-range Ising spin-bath coupling [0.0]
We study the central limit theorem of qubit dephasing in the central spin model.
We prove this approximation for a bath depicted by an Ising spin system.
We show that in certain cases, namely for short-range (exponentially decaying) coupling, this approximation breaks.
arXiv Detail & Related papers (2024-09-19T13:14:31Z) - A New Framework for Quantum Phases in Open Systems: Steady State of Imaginary-Time Lindbladian Evolution [18.47824812164327]
We introduce the concept of imaginary-time Lindbladian evolution as an alternative framework.
This new approach defines gapped quantum phases in open systems through the spectrum properties of the imaginary-Liouville superoperator.
arXiv Detail & Related papers (2024-08-06T14:53:40Z) - Adiabatic State Preparation in a Quantum Ising Spin Chain [32.352947507436355]
We report on adiabatic state preparation in the one-dimensional quantum Ising model using ultracold bosons in a tilted optical lattice.
We observe enhanced fluctuations around the transition between paramagnetic and antiferromagnetic states, marking the precursor of quantum critical behavior.
arXiv Detail & Related papers (2024-04-11T05:27:40Z) - Geometric phases along quantum trajectories [58.720142291102135]
We study the distribution function of geometric phases in monitored quantum systems.
For the single trajectory exhibiting no quantum jumps, a topological transition in the phase acquired after a cycle.
For the same parameters, the density matrix does not show any interference.
arXiv Detail & Related papers (2023-01-10T22:05:18Z) - Directly Revealing Entanglement Dynamics through Quantum Correlation
Transfer Functions with Resultant Demonstration of the Mechanism of Many-Body
Localization [0.0]
This paper introduces the Quantum Correlation Transfer Function (QCTF) approach to entanglement dynamics in many-body quantum systems.
We show that QCTF can be fully characterized directly from the system's Hamiltonian, which circumvents the bottleneck of calculating the many-body system's time-evolution.
We also show that QCTF provides a new foundation to study the Eigenstate Thermalization Hypothesis (ETH)
arXiv Detail & Related papers (2022-01-26T22:50:04Z) - Probing Topological Spin Liquids on a Programmable Quantum Simulator [40.96261204117952]
We use a 219-atom programmable quantum simulator to probe quantum spin liquid states.
In our approach, arrays of atoms are placed on the links of a kagome lattice and evolution under Rydberg blockade creates frustrated quantum states.
The onset of a quantum spin liquid phase of the paradigmatic toric code type is detected by evaluating topological string operators.
arXiv Detail & Related papers (2021-04-09T00:18:12Z) - Realising the Symmetry-Protected Haldane Phase in Fermi-Hubbard Ladders [0.0]
Topology in quantum many-body systems has profoundly changed our understanding of quantum phases of matter.
Here, we realise such a topological Haldane phase with Fermi-Hubbard ladders in an ultracold-atom quantum simulator.
arXiv Detail & Related papers (2021-03-18T17:55:56Z) - Quantum particle across Grushin singularity [77.34726150561087]
We study the phenomenon of transmission across the singularity that separates the two half-cylinders.
All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection.
This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
arXiv Detail & Related papers (2020-11-27T12:53:23Z) - Quantum Non-equilibrium Many-Body Spin-Photon Systems [91.3755431537592]
dissertation concerns the quantum dynamics of strongly-correlated quantum systems in out-of-equilibrium states.
Our main results can be summarized in three parts: Signature of Critical Dynamics, Driven Dicke Model as a Test-bed of Ultra-Strong Coupling, and Beyond the Kibble-Zurek Mechanism.
arXiv Detail & Related papers (2020-07-23T19:05:56Z) - Unraveling the topology of dissipative quantum systems [58.720142291102135]
We discuss topology in dissipative quantum systems from the perspective of quantum trajectories.
We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
arXiv Detail & Related papers (2020-07-12T11:26:02Z)
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.