Entanglement scaling and criticality of quantum many-body systems in canonical quantization picture using tensor network
- URL: http://arxiv.org/abs/2410.23624v1
- Date: Thu, 31 Oct 2024 04:20:49 GMT
- Title: Entanglement scaling and criticality of quantum many-body systems in canonical quantization picture using tensor network
- Authors: Rui Hong, Hao-Wei Cui, An-Chun Ji, Shi-Ju Ran,
- Abstract summary: This work investigates the quantum entanglement and criticality of the ground-state wave-functions of infinitely-many coupled quantum oscillators (iCQOs)
By extending the imaginary-time evolution algorithm with translationally-invariant functional tensor network, we simulate the ground state of iCQOs with the presence of two- and three-body couplings.
We reveal the logarithmic scaling law of entanglement entropy (EE) and the scaling law of correlation length against the virtual bond $chi$ at the dividing point of physical and non-physical regions.
- Score: 0.0
- License:
- Abstract: Simulating strongly-correlated quantum systems in continuous space belongs to the most challenging and long-concerned issues in quantum physics. This work investigates the quantum entanglement and criticality of the ground-state wave-functions of infinitely-many coupled quantum oscillators (iCQOs). The essential task involves solving a set of partial differential equations (Schr\"odinger equations in the canonical quantization picture) with infinitely-many variables, which currently lacks valid methods. By extending the imaginary-time evolution algorithm with translationally-invariant functional tensor network, we simulate the ground state of iCQOs with the presence of two- and three-body couplings. We determine the range of coupling strengths where there exists a real ground-state energy (dubbed as physical region). With two-body couplings, we reveal the logarithmic scaling law of entanglement entropy (EE) and the polynomial scaling law of correlation length against the virtual bond dimension $\chi$ at the dividing point of physical and non-physical regions. These two scaling behaviors are signatures of criticality, according to the previous results in quantum lattice models, but were not reported in continuous-space quantum systems. The scaling coefficients result in a central charge $c=1$, indicating the presence of free boson conformal field theory (CFT). With three-body couplings where there exist no analytical nor numerical results, we show the breakdown of CFT at the dividing point even with an extremely small strength of three-body terms. Our work uncovers the scaling behaviors of EE in the continuous-space quantum many-body systems, providing numerical evidences for the efficiency of tensor networks in representing the continuous-space quantum many-body ground states in the thermodynamic limit.
Related papers
- Probing critical phenomena in open quantum systems using atom arrays [3.365378662696971]
At quantum critical points, correlations decay as a power law, with exponents determined by a set of universal scaling dimensions.
Here, we employ a Rydberg quantum simulator to adiabatically prepare critical ground states of both a one-dimensional ring and a two-dimensional square lattice.
By accounting for and tuning the openness of our quantum system, we are able to directly observe power-law correlations and extract the corresponding scaling dimensions.
arXiv Detail & Related papers (2024-02-23T15:21:38Z) - Probing Confinement Through Dynamical Quantum Phase Transitions: From
Quantum Spin Models to Lattice Gauge Theories [0.0]
We show that a change in the type of dynamical quantum phase transitions accompanies the confinement-deconfinement transition.
Our conclusions can be tested in modern quantum-simulation platforms, such as ion-trap setups and cold-atom experiments of gauge theories.
arXiv Detail & Related papers (2023-10-18T18:00:04Z) - Cubic* criticality emerging from a quantum loop model on triangular lattice [5.252398154171938]
We show that the triangular lattice quantum loop model (QLM) hosts a rich ground state phase diagram with nematic, vison plaquette (VP) crystals, and the $mathbb$ quantum spin liquid (QSL) close to the Rokhsar-Kivelson quantum critical point.
These solutions are of immediate relevance to both statistical and quantum field theories, as well as the rapidly growing experiments in Rydberg atom arrays and quantum moir'e materials.
arXiv Detail & Related papers (2023-09-11T18:00:05Z) - Universality of critical dynamics with finite entanglement [68.8204255655161]
We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement.
Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
arXiv Detail & Related papers (2023-01-23T19:23:54Z) - Multiscale space-time ansatz for correlation functions of quantum
systems based on quantics tensor trains [1.231476564107544]
Correlation functions of quantum systems are defined in high-dimensional space-time domains.
We propose a multi-scale space-time ansatz for correlation functions of quantum systems based on quantics tensor trains.
arXiv Detail & Related papers (2022-10-24T07:17:02Z) - Quantum Davidson Algorithm for Excited States [42.666709382892265]
We introduce the quantum Krylov subspace (QKS) method to address both ground and excited states.
By using the residues of eigenstates to expand the Krylov subspace, we formulate a compact subspace that aligns closely with the exact solutions.
Using quantum simulators, we employ the novel QDavidson algorithm to delve into the excited state properties of various systems.
arXiv Detail & Related papers (2022-04-22T15:03:03Z) - Probing quantum information propagation with out-of-time-ordered
correlators [41.12790913835594]
Small-scale quantum information processors hold the promise to efficiently emulate many-body quantum systems.
Here, we demonstrate the measurement of out-of-time-ordered correlators (OTOCs)
A central requirement for our experiments is the ability to coherently reverse time evolution.
arXiv Detail & Related papers (2021-02-23T15:29:08Z) - 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) - Quantum Statistical Complexity Measure as a Signalling of Correlation
Transitions [55.41644538483948]
We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions.
We apply our measure to two exactly solvable Hamiltonian models, namely: the $1D$-Quantum Ising Model and the Heisenberg XXZ spin-$1/2$ chain.
We also compute this measure for one-qubit and two-qubit reduced states for the considered models, and analyse its behaviour across its quantum phase transitions for finite system sizes as well as in the thermodynamic limit by using Bethe ansatz.
arXiv Detail & Related papers (2020-02-05T00:45:21Z) - Einselection from incompatible decoherence channels [62.997667081978825]
We analyze an open quantum dynamics inspired by CQED experiments with two non-commuting Lindblad operators.
We show that Fock states remain the most robust states to decoherence up to a critical coupling.
arXiv Detail & Related papers (2020-01-29T14:15:19Z)
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.