Publications

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Rapid detection of phase transitions from Monte Carlo samples before equilibrium

Jiewei Ding, Ho-Kin Tang, Wing Chi Yu

SciPost Phys. 13, 057 (2022) · published 9 September 2022 | · pdf

We found that Bidirectional LSTM and Transformer can classify different phases of condensed matter models and determine the phase transition points by learning features in the Monte Carlo raw data before equilibrium. Our method can significantly reduce the time and computational resources required for probing phase transitions as compared to the conventional Monte Carlo simulation. We also provide evidence that the method is robust and the performance of the deep learning model is insensitive to the type of input data (we tested spin configurations of classical models and green functions of a quantum model), and it also performs well in detecting Kosterlitz–Thouless phase transitions.
Stochastic series expansion quantum Monte Carlo for Rydberg arrays

Ejaaz Merali, Isaac J. S. De Vlugt, Roger G. Melko

SciPost Phys. Core 7, 016 (2024) · published 5 April 2024 | · pdf

Arrays of Rydberg atoms are a powerful platform to realize strongly-interacting quantum many-body systems. A common Rydberg Hamiltonian is free of the sign problem, meaning that its equilibrium properties are amenable to efficient simulation by quantum Monte Carlo (QMC). In this paper, we develop a Stochastic Series Expansion QMC algorithm for Rydberg atoms interacting on arbitrary lattices. We describe a cluster update that allows for the efficient sampling and calculation of physical observables for typical experimental parameters, and show that the algorithm can reproduce experimental results on large Rydberg arrays in one and two dimensions.
Inferring effective couplings with restricted Boltzmann machines

Aurélien Decelle, Cyril Furtlehner, Alfonso De Jesús Navas Gómez, Beatriz Seoane

SciPost Phys. 16, 095 (2024) · published 5 April 2024 | · pdf

Generative models offer a direct way of modeling complex data. Energy-based models attempt to encode the statistical correlations observed in the data at the level of the Boltzmann weight associated with an energy function in the form of a neural network. We address here the challenge of understanding the physical interpretation of such models. In this study, we propose a simple solution by implementing a direct mapping between the Restricted Boltzmann Machine and an effective Ising spin Hamiltonian. This mapping includes interactions of all possible orders, going beyond the conventional pairwise interactions typically considered in the inverse Ising (or Boltzmann Machine) approach, and allowing the description of complex datasets. Earlier works attempted to achieve this goal, but the proposed mappings were inaccurate for inference applications, did not properly treat the complexity of the problem, or did not provide precise prescriptions for practical application. To validate our method, we performed several controlled inverse numerical experiments in which we trained the RBMs using equilibrium samples of predefined models with local external fields, 2-body and 3-body interactions in different sparse topologies. The results demonstrate the effectiveness of our proposed approach in learning the correct interaction network and pave the way for its application in modeling interesting binary variable datasets. We also evaluate the quality of the inferred model based on different training methods.
Phase transitions of wave packet dynamics in disordered non-Hermitian systems

Helene Spring, Viktor Könye, Fabian A. Gerritsma, Ion Cosma Fulga, Anton R. Akhmerov

SciPost Phys. 16, 120 (2024) · published 3 May 2024 | · pdf

Disorder can localize the eigenstates of one-dimensional non-Hermitian systems, leading to an Anderson transition with a critical exponent of 1. We show that, due to the lack of energy conservation, the dynamics of individual, real-space wave packets follows a different behavior. Both transitions between localization and unidirectional amplification, as well as transitions between distinct propagating phases become possible. The critical exponent of the transition is close to 1/2 in propagating-propagating and (de)localization transitions.
Thermalization of long range Ising model in different dynamical regimes: A full counting statistics approach

Nishan Ranabhat, Mario Collura

SciPost Phys. Core 7, 017 (2024) · published 5 April 2024 | · pdf

We study the thermalization of the transverse field Ising chain with a power law decaying interaction $\sim 1/r^{\alpha}$ following a global quantum quench of the transverse field in two different dynamical regimes. The thermalization behavior is quantified by comparing the full probability distribution function (PDF) of the evolving states with the corresponding thermal state given by the canonical Gibbs ensemble (CGE). To this end, we used the matrix product state (MPS)-based Time Dependent Variational Principle (TDVP) algorithm to simulate both real time evolution following a global quantum quench and the finite temperature density operator. We observe that thermalization is strongly suppressed in the region with strong confinement for all interaction strengths $\alpha$, whereas thermalization occurs in the region with weak confinement.
Spatial separation of spin currents in transition metal dichalcogenides

Antonio L. R. Manesco, Artem Pulkin

SciPost Phys. Core 6, 036 (2023) · published 1 May 2023 | · pdf

We theoretically predict spatial separation of spin-polarized ballistic currents in transition metal dichalcogenides (TMDs) due to trigonal warping. We quantify the effect in terms of spin polarization of charge carrier currents in a prototypical 3-terminal ballistic device where spin-up and spin-down charge carriers are collected by different leads. We show that the magnitude of the current spin polarization depends strongly on the charge carrier energy and the direction with respect to crystallographic orientations in the device. We study the (negative) effect of lattice imperfections and disorder on the observed spin polarization. Our investigation provides an avenue towards observing spin discrimination in a defect-free time reversal-invariant material.
Thermal pure matrix product state in two dimensions: Tracking thermal equilibrium from paramagnet down to the Kitaev honeycomb spin liquid state

Matthias Gohlke, Atsushi Iwaki, Chisa Hotta

SciPost Phys. 15, 206 (2023) · published 24 November 2023 | · pdf

We present the first successful application of the matrix product state (MPS) representing a thermal quantum pure state (TPQ) in equilibrium in two spatial dimensions over almost the entire temperature range. We use the Kitaev honeycomb model as a prominent example hosting a quantum spin liquid (QSL) ground state to target the two specific-heat peaks previously solved nearly exactly using the free Majorana fermionic description. Starting from the high-temperature random state, our TPQ-MPS framework on a cylinder precisely reproduces these peaks, showing that the quantum many-body description based on spins can still capture the emergent itinerant Majorana fermions in a ${\mathbb Z}_2$ gauge field. The truncation process efficiently discards the high-energy states, eventually reaching the long-range entangled topological state approaching the exact ground state for a given finite size cluster. An advantage of TPQ-MPS over exact diagonalization or purification-based methods is its lowered numerical cost coming from a reduced effective Hilbert space even at finite temperature.
Interpolating between the gauge and Schrödinger pictures of quantum dynamics

Sayak Guha Roy, Kevin Slagle

SciPost Phys. Core 6, 081 (2023) · published 24 November 2023 | · pdf

Although spatial locality is explicit in the Heisenberg picture of quantum dynamics, spatial locality is not explicit in the Schrödinger picture equations of motion. The gauge picture is a modification of Schrödinger's picture such that locality is explicit in the equations of motion. In order to achieve this explicit locality, the gauge picture utilizes (1) a distinct wavefunction associated with each patch of space, and (2) time-dependent unitary connections to relate the Hilbert spaces associated with nearby patches. In this work, we show that by adding an additional spatially-local term to the gauge picture equations of motion, we can effectively interpolate between the gauge and Schrödinger pictures, such that when this additional term has a large coefficient, all of the gauge picture wavefunctions approach the Schrödginer picture wavefunction (and the connections approach the identity).
Floquet engineering of axion and high-Chern number phases in a topological insulator under illumination

Mohammad Shafiei, Farhad Fazileh, François M. Peeters, Milorad V. Milošević

SciPost Phys. Core 7, 024 (2024) · published 1 May 2024 | · pdf

Quantum anomalous Hall, high-Chern number, and axion phases in topological insulators are characterized by its Chern invariant C (respectively, C=1, integer C>1, and C=0 with half-quantized Hall conductance of opposite signs on top and bottom surfaces). They are of recent interest because of novel fundamental physics and prospective applications, but identifying and controlling these phases has been challenging in practice. Here we show that these states can be created and switched between in thin films of Bi$_2$Se$_3$ by Floquet engineering, using irradiation by circularly polarized light. We present the calculated phase diagrams of encountered topological phases in Bi$_2$Se$_3$, as a function of wavelength and amplitude of light, as well as sample thickness, after properly taking into account the penetration depth of light and the variation of the gap in the surface states. These findings open pathways towards energy-efficient optoelectronics, advanced sensing, quantum information processing and metrology.
Traveling/non-traveling phase transition and non-ergodic properties in the random transverse-field Ising model on the Cayley tree

Ankita Chakrabarti, Cyril Martins, Nicolas Laflorencie, Bertrand Georgeot, Éric Brunet, Gabriel Lemarié

SciPost Phys. 15, 211 (2023) · published 28 November 2023 | · pdf

We study the random transverse field Ising model on a finite Cayley tree. This enables us to probe key questions arising in other important disordered quantum systems, in particular the Anderson transition and the problem of dirty bosons on the Cayley tree, or the emergence of non-ergodic properties in such systems. We numerically investigate this problem building on the cavity mean-field method complemented by state-of-the art finite-size scaling analysis. Our numerics agree very well with analytical results based on an analogy with the traveling wave problem of a branching random walk in the presence of an absorbing wall. Critical properties and finite-size corrections for the zero-temperature paramagnetic-ferromagnetic transition are studied both for constant (independent of the system volume) and algebraically vanishing (scaling as an inverse power law with the system volume) boundary conditions. In the later case, we reveal a regime which is reminiscent of the non-ergodic delocalized phase observed in other systems, thus shedding some light on critical issues in the context of disordered quantum systems, such as Anderson transitions, the many-body localization or disordered bosons in infinite dimensions.

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