Publications

Order by: publication date number of citations

• On the generalizability of artificial neural networks in spin models

  Hon Man Yau, Nan Su

  SciPost Phys. Core 5, 032 (2022) · published 8 June 2022 | Toggle abstract · pdf

  The applicability of artificial neural networks (ANNs) is typically limited to the models they are trained with and little is known about their generalizability, which is a pressing issue in the practical application of trained ANNs to unseen problems. Here, by using the task of identifying phase transitions in spin models, we establish a systematic generalizability such that simple ANNs trained with the two-dimensional ferromagnetic Ising model can be applied to the ferromagnetic q-state Potts model in different dimensions for q>=2. The same scheme can be applied to the highly nontrivial antiferromagnetic q-state Potts model. We demonstrate that similar results can be obtained by reducing the exponentially large state space spanned by the training data to one that comprises only three representative configurations artificially constructed through symmetry considerations. We expect our findings to simplify and accelerate the development of machine learning-assisted tasks in spin-model related disciplines in physics and materials science.

  6 citations

• Critical properties of quantum three- and four-state Potts models with boundaries polarized along the transverse field

  Natalia Chepiga

  SciPost Phys. Core 5, 031 (2022) · published 30 May 2022 | Toggle abstract · pdf

  By computing the low-lying energy excitation spectra with the density matrix renormalization group algorithm we show that boundaries polarized in the direction of the transverse field lead to scale-invariant conformal towers of states at the critical point of the quantum four-state Potts model - a special symmetric case of the Ashkin-Teller model. Furthermore, by direct comparison of the excitation spectra we phenomenologically establish the duality between the transverse-polarized and three-state-mixed boundary conditions at the four-state Potts critical point. Finally, for completeness, we verify that in the quantum three-state Potts model the "new" boundary conditions dual to the mixed ones can be realized by polarizing edge spins along the transverse field.

  7 citations

• Adaptive numerical solution of Kadanoff-Baym equations

  Francisco Meirinhos, Michael Kajan, Johann Kroha, Tim Bode

  SciPost Phys. Core 5, 030 (2022) · published 27 May 2022 | Toggle abstract · pdf

  A time-stepping scheme with adaptivity in both the step size and the integration order is presented in the context of non-equilibrium dynamics described via Kadanoff-Baym equations. The accuracy and effectiveness of the algorithm are analysed by obtaining numerical solutions of exactly solvable models. We find a significant reduction in the number of time-steps compared to fixed-step methods. Due to the at least quadratic scaling of Kadanoff-Baym equations, reducing the amount of steps can dramatically increase the accessible integration time, opening the door for the study of long-time dynamics in interacting systems. A selection of illustrative examples is provided, among them interacting and open quantum systems as well as classical stochastic processes. An open-source implementation of our algorithm in the scientific-computing language Julia is made available.

  18 citations

• Landau levels in curved space realized in strained graphene

  Glenn Wagner, Fernando de Juan, Dung X. Nguyen

  SciPost Phys. Core 5, 029 (2022) · published 23 May 2022 | Toggle abstract · pdf

  The quantum Hall effect in curved space has been the subject of many theoretical investigations in the past, but devising a physical system to observe this effect is hard. Many works have indicated that electronic excitations in strained graphene realize Dirac fermions in curved space in the presence of a background pseudo-gauge field, providing an ideal playground for this. However, the absence of a direct matching between a numerical, strained tight-binding calculation of an observable and the corresponding curved space prediction has hindered realistic predictions. In this work, we provide this matching by deriving the low-energy Hamiltonian from the tight-binding model analytically to second order in the strain and mapping it to the curved-space Dirac equation. Using a strain profile that produces a constant pseudo-magnetic field and a constant curvature, we compute the Landau level spectrum with real-space numerical tight-binding calculations and find excellent agreement with the prediction of the quantum Hall effect in curved space. We conclude discussing experimental schemes for measuring this effect.

  8 citations

• Do Drinfeld twists of $AdS_5 \times S^5$ survive light-cone quantization?

  Stijn J. van Tongeren, Yannik Zimmermann

  SciPost Phys. Core 5, 028 (2022) · published 19 May 2022 | Toggle abstract · pdf

  We study how a wide class of Abelian Yang-Baxter deformations of the AdS$_\mathsf{5} \times $S$^\mathsf{5}$ string behave at the quantum level. These deformations are equivalent to TsT transformations and conjectured to be dual to beta, dipole, and noncommutative deformations of SYM. Classically they correspond to Drinfeld twists of the original theory. To verify this expectation at the quantum level we compute and match (1) the bosonic two-body tree-level worldsheet scattering matrix of these deformations in the uniform light-cone gauge, and (2) the Bethe equations of the equivalent model with twisted boundary conditions. We find that for a generalization of gamma deformations of the BMN string the we are able to express the S matrix either through a Drinfeld twist or a shift of momenta. For deformations of the GKP string around the null-cusp solution we encounter calculational obstacles that prevent us from calculating the scattering matrix.

  8 citations

• Exact dynamical correlations of nonlocal operators in quadratic open Fermion systems: a characteristic function approach

  Qing-Wei Wang

  SciPost Phys. Core 5, 027 (2022) · published 3 May 2022 | Toggle abstract · pdf

  The dynamical correlations of nonlocal operators in general quadratic open fermion systems is still a challenging problem. Here we tackle this problem by developing a new formulation of open fermion many-body systems, namely, the characteristic function approach. Illustrating the technique, we analyze a finite Kitaev chain with boundary dissipation and consider anyon-type nonlocal excitations. We give explicit formula for the Green's functions, demonstrating an asymmetric light cone induced by the anyon statistical parameter and an increasing relaxation rate with this parameter. We also analyze some other types of nonlocal operator correlations such as the full counting statistics of the charge number and the Loschmidt echo in a quench from the vacuum state. The former shows clear signature of a nonequilibrium quantum phase transition, while the later exhibits cusps at some critical times and hence demonstrates dynamical quantum phase transitions.

  6 citations

• From integrability to chaos in quantum Liouvillians

  Álvaro Rubio-García, Rafael A. Molina, Jorge Dukelsky

  SciPost Phys. Core 5, 026 (2022) · published 2 May 2022 | Toggle abstract · pdf

  The dynamics of open quantum systems can be described by a Liouvillian, which in the Markovian approximation fulfills the Lindblad master equation. We present a family of integrable many-body Liouvillians based on Richardson-Gaudin models with a complex structure of the jump operators. Making use of this new region of integrability, we study the transition to chaos in terms of a two-parameter Liouvillian. The transition is characterized by the spectral statistics of the complex eigenvalues of the Liouvillian operators using the nearest neighbor spacing distribution and by the ratios between eigenvalue distances.

  23 citations

• Many-body Bell inequalities for bosonic qubits

  Jan Chwedenczuk

  SciPost Phys. Core 5, 025 (2022) · published 29 April 2022 | Toggle abstract · pdf

  Since John Bell formulated his paramount inequality for a pair of spin-$1/2$ particles, quantum mechanics has been confronted with the postulates of local realism with various equivalent configurations. Current technology, with its advanced manipulation and detection methods, allows to extend the Bell tests to more complex structures. The aim of this work is to analyze a set of Bell inequalities suitable for a possibly broad family of many-body systems with the focus on bosonic qubits. We develop a method that allows for a step-by-step study of the many-body Bell correlations, for instance among atoms forming a two-mode Bose-Einstein condensate or between photons obtained from the parametric-down conversion. The presented approach is valid both for cases of fixed and non-fixed number of particles, hence it allows for a thorough analysis of quantum correlations in a variety of many-body systems.

  8 citations

• Crystalline Weyl semimetal phase in Quantum Spin Hall systems under magnetic fields

  Fernando Dominguez, Benedikt Scharf, Ewelina M. Hankiewicz

  SciPost Phys. Core 5, 024 (2022) · published 28 April 2022 | Toggle abstract · pdf

  We investigate an unconventional topological phase transition that occurs in quantum spin Hall (QSH) systems when applying an external in-plane magnetic field. We show that this transition between QSH and trivial insulator phases is separated by a stable topological gapless phase, which is protected by the combination of particle-hole and reflection symmetries, and thus, we dub it as crystalline Weyl semimetal. We explore the stability of this new phase when particle-hole symmetry breaking terms are present. Especially, we predict a robust unconventional topological phase transition to be visible for materials described by Kane and Mele model even if particle-hole symmetry is significantly broken.

  5 citations

• Measurement-induced criticality in extended and long-range unitary circuits

  Shraddha Sharma, Xhek Turkeshi, Rosario Fazio, Marcello Dalmonte

  SciPost Phys. Core 5, 023 (2022) · published 21 April 2022 | Toggle abstract · pdf

  We explore the dynamical phases of unitary Clifford circuits with variable-range interactions, coupled to a monitoring environment. We investigate two classes of models, distinguished by the action of the unitary gates, which either are organized in clusters of finite-range two-body gates, or are pair-wise interactions randomly distributed throughout the system with a power-law distribution. We find the range of the interactions plays a key role in characterizing both phases and their measurement-induced transitions. For the cluster unitary gates we find a transition between a phase with volume-law scaling of the entanglement entropy and a phase with area-law entanglement entropy. Our results indicate that the universality class of the phase transition is compatible to that of short range hybrid Clifford circuits. Oppositely, in the case of power-law distributed gates, we find the universality class of the phase transition changes continuously with the parameter controlling the range of interactions. In particular, for intermediate values of the control parameter, we find a non-conformal critical line which separates a phase with volume-law scaling of the entanglement entropy from one with sub-extensive scaling. Within this region, we find the entanglement entropy and the logarithmic negativity present a cross-over from a phase with algebraic growth of entanglement with system size, and an area-law phase.

  78 citations