Quantum-critical properties of the long-range transverse-field Ising
model from quantum Monte Carlo simulations
- URL: http://arxiv.org/abs/2103.09469v1
- Date: Wed, 17 Mar 2021 07:00:29 GMT
- Title: Quantum-critical properties of the long-range transverse-field Ising
model from quantum Monte Carlo simulations
- Authors: J. Koziol, A. Langheld, S.C. Kapfer, and K.P. Schmidt
- Abstract summary: The quantum-critical properties of the transverse-field Ising model are investigated by means of quantum Monte Carlo.
For ferromagnetic Ising interactions, we resolve the limiting regimes known from field theory, ranging from the nearest-neighbor Ising to the long-range universality classes.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The quantum-critical properties of the transverse-field Ising model with
algebraically decaying interactions are investigated by means of stochastic
series expansion quantum Monte Carlo, on both the one-dimensional linear chain
and the two-dimensional square lattice. We extract the critical exponents $\nu$
and $\beta$ as a function of the decay exponent of the long-range interactions.
For ferromagnetic Ising interactions, we resolve the limiting regimes known
from field theory, ranging from the nearest-neighbor Ising to the long-range
Gaussian universality classes, as well as the intermediate regime with
continuously varying critical exponents. In the long-range Gaussian regime, we
treat the effect of dangerous irrelevant variables on finite-size scaling
forms. For antiferromagnetic and therefore competing Ising interactions, the
stochastic series expansion algorithm displays growing auto-correlation times
leading to a reduced performance. Nevertheless, our results are consistent with
the nearest-neighbor Ising universality for all investigated interaction ranges
both on the linear chain and the square lattice.
Related papers
- 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) - Quantum-critical properties of the one- and two-dimensional random transverse-field Ising model from large-scale quantum Monte Carlo simulations [0.0]
We study the ferromagnetic transverse-field Ising model with quenched disorder at $T = 0$ in one and two dimensions.
The emphasis on effective zero-temperature simulations resolves several inconsistencies in existing literature.
arXiv Detail & Related papers (2024-03-08T11:20:42Z) - Stochastic parameter optimization analysis of dynamical quantum critical phenomena in long-range transverse-field Ising chain [0.0]
We explore the quantum phase transition of the one-dimensional long-range transverse-field Ising model.
In our simulations, the simulator automatically determines the parameters to sample from, even without prior knowledge of the critical point and universality class.
We successfully determine the universality boundary between the latter two as $sigma = 7/4$ based on the dynamical exponent.
arXiv Detail & Related papers (2023-05-23T14:46:16Z) - Continuously varying critical exponents in long-range quantum spin
ladders [0.0]
We investigate the quantum-critical behavior between the rung-singlet phase with hidden string order and the N'eel phase with broken $SU(2)$-symmetry on quantum spin ladders.
A non-trivial regime of continuously varying critical exponents as well as long-range mean-field behavior is demonstrated.
arXiv Detail & Related papers (2022-09-02T17:23:58Z) - Quantum chaos and thermalization in the two-mode Dicke model [77.34726150561087]
We discuss the onset of quantum chaos and thermalization in the two-mode Dicke model.
The two-mode Dicke model exhibits normal to superradiant quantum phase transition.
We show that the temporal fluctuations of the expectation value of the collective spin observable around its average are small and decrease with the effective system size.
arXiv Detail & Related papers (2022-07-08T11:16:29Z) - Decimation technique for open quantum systems: a case study with
driven-dissipative bosonic chains [62.997667081978825]
Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics.
We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function.
We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
arXiv Detail & Related papers (2022-02-15T19:00:09Z) - Exact Continuum Representation of Long-range Interacting Systems and
Emerging Exotic Phases in Unconventional Superconductors [0.0]
We put forth an exact representation of long-range interacting lattices that separates the model into a term describing its continuous analog, the integral contribution, and a term that fully resolves the microstructure.
We employ our representation in Fourier space to solve the important problem of long-range interacting unconventional superconductors.
We show that the interactions can be used to fine-tune the Higgs mode's stability, ranging from exponential decay of the oscillation amplitude up to complete stabilization.
arXiv Detail & Related papers (2022-01-26T18:16:51Z) - Out-of-time-order correlations and the fine structure of eigenstate
thermalisation [58.720142291102135]
Out-of-time-orderors (OTOCs) have become established as a tool to characterise quantum information dynamics and thermalisation.
We show explicitly that the OTOC is indeed a precise tool to explore the fine details of the Eigenstate Thermalisation Hypothesis (ETH)
We provide an estimation of the finite-size scaling of $omega_textrmGOE$ for the general class of observables composed of sums of local operators in the infinite-temperature regime.
arXiv Detail & Related papers (2021-03-01T17:51:46Z) - Spreading of Correlations and Entanglement in the Long-Range Transverse
Ising Chain [0.0]
Long-range interactions allow for a form of causality in non-relativistic quantum models.
We show that a weak form of causality emerges, characterized by non-universal dynamical exponents.
Our results shed light on the propagation of information in long-range interacting lattice models.
arXiv Detail & Related papers (2020-11-23T09:30:06Z) - Operator-algebraic renormalization and wavelets [62.997667081978825]
We construct the continuum free field as the scaling limit of Hamiltonian lattice systems using wavelet theory.
A renormalization group step is determined by the scaling equation identifying lattice observables with the continuum field smeared by compactly supported wavelets.
arXiv Detail & Related papers (2020-02-04T18:04:51Z) - From stochastic spin chains to quantum Kardar-Parisi-Zhang dynamics [68.8204255655161]
We introduce the asymmetric extension of the Quantum Symmetric Simple Exclusion Process.
We show that the time-integrated current of fermions defines a height field which exhibits a quantum non-linear dynamics.
arXiv Detail & Related papers (2020-01-13T14:30:36Z)
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.