Publications

Order by: publication date number of citations

• Functional renormalization group for fermions on a one dimensional lattice at arbitrary filling

  Lucas Désoppi, Nicolas Dupuis, Claude Bourbonnais

  SciPost Phys. 17, 054 (2024) · published 15 August 2024 | Toggle abstract · pdf

  A formalism based on the fermionic functional-renormalization-group approach to interacting electron models defined on a lattice is presented. One-loop flow equations for the coupling constants and susceptibilities in the particle-particle and particle-hole channels are derived in weak-coupling conditions. It is shown that lattice effects manifest themselves through the curvature of the spectrum and the dependence of the coupling constants on momenta. This method is then applied to the one-dimensional extended Hubbard model; we thoroughly discuss the evolution of the phase diagram, and in particular the fate of the bond-centered charge-density-wave phase, as the system is doped away from half-filling. Our findings are compared to the predictions of the field-theory continuum limit and available numerical results.

• Quantum robustness of the toric code in a parallel field on the honeycomb and triangular lattice

  Viktor Kott, Matthias Mühlhauser, Jan Alexander Koziol, Kai Phillip Schmidt

  SciPost Phys. 17, 053 (2024) · published 15 August 2024 | Toggle abstract · pdf

  We investigate the quantum robustness of the topological order in the toric code on the honeycomb lattice in the presence of a uniform parallel field. For a field in $z$-direction, the low-energy physics is in the flux-free sector and can be mapped to the transverse-field Ising model on the honeycomb lattice. One finds a second-order quantum phase transition in the 3D Ising$^\star$ universality class for both signs of the field. The same is true for a postive field in $x$-direction where an analogue mapping in the charge-free sector yields a ferromagnetic transverse-field Ising model on the triangular lattice and the phase transition is still 3D Ising$^\star$. In contrast, for negative $x$-field, the charge-free sector is mapped to the highly frustrated antiferromagnetic transverse-field Ising model on the triangular lattice which is known to host a quantum phase transition in the 3D XY$^\star$ universality class. Further, the charge-free sector does not always contain the low-energy physics for negative $x$-fields and a first-order phase transition to the polarized phase in the charge-full sector takes place at larger negative field values. We quantify the location of this transition by comparing quantum Monte Carlo simulations and high-field series expansions. The full extension of the topological phase in the presence of $x$- and $z$-fields is determined by perturbative linked-cluster expansions using a full graph decomposition. Extrapolating the high-order series of the charge and the flux gap allows to estimate critical exponents of the gap closing. This analysis indicates that the topological order breaks down by critical lines of 3D Ising$^\star$ and 3D XY$^\star$ type with interesting potential multi-critical crossing points. All findings for the toric code on the honeycomb lattice can be transferred exactly to the toric code on the triangular lattice.

• Constraints on the spectrum of field theories with non-integer $O(N)$ symmetry from quantum evanescence

  Weiguang Cao, Xiaochuan Lu, Tom Melia

  SciPost Phys. Core 7, 055 (2024) · published 14 August 2024 | Toggle abstract · pdf

  We identify constraints in the energy spectra of quantum theories that have a global $O(N)$ symmetry, where $N$ is treated as a continuous parameter. We point out that a class of evanescent states fall out of the spectrum at integer values of $N$ in pairs, via an annihilation mechanism. This forces the energies of the states in such a pair to approach equality as $N$ approaches a certain integer, with both states disappearing at precisely integer $N$ and the point of would-be degeneracy. These constraints occur between different irreducible representations of the analytic continuation of $O(N)$ and hold non-perturbatively. We give examples in the spectra of the critical $O(N)$ model.

• Localized dopant motion across the 2D Ising phase transition

  Kristian Knakkergaard Nielsen

  SciPost Phys. Core 7, 054 (2024) · published 14 August 2024 | Toggle abstract · pdf

  I investigate the motion of a single hole in 2D spin lattices with square and triangular geometries. While the spins have nearest neighbor Ising spin couplings $J$, the hole is allowed to move only in 1D along a single line in the 2D lattice with nearest neighbor hopping amplitude $t$. The non-equilibrium hole dynamics is initialized by suddenly removing a single spin from the thermal Ising spin lattice. I find that for any nonzero spin coupling and temperature, the hole is localized. This is an extension of the thermally induced localization phenomenon [Phys. Rev. Res. 6, 023325 (2024)] to the case, where there is a phase transition to a long-range ordered ferromagnetic phase. The dynamics depends only on the ratio of the temperature to the spin coupling, $k_BT / |J|$, and on the ratio of the spin coupling to the hopping $J/t$. I characterize these dependencies in great detail. In particular, I find universal behavior at high temperatures, common features for the square and triangular lattices across the Curie temperatures for ferromagnetic interactions, and highly distinct behaviors for the two geometries in the presence of antiferromagnetic interactions due geometric frustration in the triangular lattice.

• Top-down and bottom-up: Studying the SMEFT beyond leading order in $1/\Lambda^2$

  Tyler Corbett

  SciPost Phys. Core 7, 053 (2024) · published 14 August 2024 | Toggle abstract · pdf

  In order to assess the relevance of higher order terms in the Standard Model effective field theory (SMEFT) expansion we consider four new physics models and their impact on the Drell Yan cross section. Of these four, one scalar model has no effect on Drell Yan, a model of fermions while appearing to generate a momentum expansion actually belongs to the vacuum expectation value expansion and so has a nominal effect on the process. The remaining two, a leptoquark and a $Z'$ model exhibit a momentum expansion. After matching these models to dimension-ten we study the how the inclusion of dimension-eight and dimension-ten operators in hypothetical effective field theory fits to the full ultraviolet models impacts fits. We do this both in the top-down approach, and in a very limited approximation to the bottom up approach of the SMEFT to infer the impact of a fully general fit to the SMEFT. We find that for the more weakly coupled models a strictly dimension-six fit is sufficient. In contrast when stronger interactions or lighter masses are considered the inclusion of dimension-eight operators becomes necessary. However, their Wilson coefficients perform the role of nuisance parameters with best fit values which can differ statistically from the theory prediction. In the most strongly coupled theories considered (which are already ruled out by data) the inclusion of dimension-ten operators allows for the measurement of dimension-eight operator coefficients consistent with theory predictions and the dimension-ten operator coefficients then behave as nuisance parameters. We also study the impact of the inclusion of partial next order results, such as dimension-six squared contributions, and find that in some cases they improve the convergence of the series while in others they hinder it.

• Dissipative preparation of a Floquet topological insulator in an optical lattice via bath engineering

  Alexander Schnell, Christof Weitenberg, André Eckardt

  SciPost Phys. 17, 052 (2024) · published 14 August 2024 | Toggle abstract · pdf

  Floquet engineering is an important tool for realizing topologically nontrivial band structures for charge-neutral atoms in optical lattices. However, the preparation of a topological-band-insulator-type state of fermions, with one nontrivial quasi-energy band filled completely and the others empty, is challenging as a result of both driving induced heating as well as imperfect adiabatic state preparation (with the latter induced by the unavoidable gap closing when passing the topological transition). An alternative procedure that has been proposed is to prepare such states dissipatively, i.e. as a steady state that emerges when coupling the system to reservoirs. Here we discuss a concrete scheme that couples the system to a weakly interacting Bose condensate given by second atomic species acting as a heat bath. Our strategy relies on the engineering of the potential for the bath particles, so that they occupy weakly coupled tubes perpendicular to the two-dimensional system. Using Floquet-Born-Markov theory, we show that the resulting nonequilibrium steady state of the driven-dissipative system approximates a topological insulator. We even find indications for the approximate stabilization of an anomalous Floquet topological insulator, a state that is impossible to realize in equilibrium.

• Closed universes in two dimensional gravity

  Mykhaylo Usatyuk, Zi-Yue Wang, Ying Zhao

  SciPost Phys. 17, 051 (2024) · published 14 August 2024 | Toggle abstract · pdf

  We study closed universes in simple models of two dimensional gravity, such as Jackiw-Teiteilboim (JT) gravity coupled to matter, and a toy topological model that captures the key features of the former. We find there is a stark contrast, as well as some connections, between the perturbative and non-perturbative aspects of the theory. We find rich semi-classical physics. However, when non-perturbative effects are included there is a unique closed universe state in each theory. We discuss possible meanings and interpretations of this observation.

  2 citations

• Normative approaches to neural coding and behavior

  Ann Hermundstad

  SciPost Phys. Lect. Notes 83 (2024) · published 13 August 2024 | Toggle abstract · pdf

  These are a brief set of lectures notes for lectures given at the Les Houches Summer School in Theoretical Biological Physics in July 2023. In these notes, I provide an introduction to some of the theoretical frameworks that are used to understand how the brain makes sense of incoming signals from the environment to ultimately guide effective behavior. I then discuss how we can apply these frameworks to understand the structure and function of real brains.

• Heavy-light $N+1$ clusters of two-dimensional fermions

  Jules Givois, Andrea Tononi, Dmitry S. Petrov

  SciPost Phys. 17, 050 (2024) · published 13 August 2024 | Toggle abstract · pdf

  We study binding of $N$ identical heavy fermions by a light atom in two dimensions assuming zero-range attractive heavy-light interactions. By using the mean-field theory valid for large $N$ we show that the $N+1$ cluster is bound when the mass ratio exceeds $1.074N^2$. The mean-field theory, being scale invariant in two dimensions, predicts only the shapes of the clusters leaving their sizes and energies undefined. By taking into account beyond-mean-field effects we find closed-form expressions for these quantities. We also discuss differences between the Thomas-Fermi and Hartree-Fock approaches for treating the heavy fermions.

  1 citation

• Quenched dynamics and pattern formation in clean and disordered Bogoliubov-de Gennes superconductors

  Bo Fan, Antonio Miguel García García

  SciPost Phys. 17, 049 (2024) · published 13 August 2024 | Toggle abstract · pdf

  We study the quench dynamics of a two dimensional superconductor in a square lattice of size up to $200× 200$ employing the self-consistent time dependent Bogoliubov-de Gennes (BdG) formalism. In the clean limit, the dynamics of the order parameter for short times, characterized by a fast exponential growth and an oscillatory pattern, agrees with the Bardeen-Cooper-Schrieffer (BCS) prediction. However, unlike BCS, we observe for longer times a universal exponential decay of these time oscillations. We show explicitly that the origin of this exponential decay is the full emergence of spatial inhomogeneities of the order parameter characterized by the exponential growth of its variance. The addition of a weak disorder does not alter these results qualitatively. In this region, the spatial inhomogeneities rapidly develop into an intricate spatial structure consisting of ordered fragmented stripes in perpendicular directions where the order parameter is heavily suppressed. As the disorder strength increases, the fragmented stripes gradually turn into a square lattice of approximately circular spatial regions where the condensate is heavily suppressed. A further increase of disorder leads to the deformation and ultimate destruction of this lattice. We show these emergent spatial patterns are sensitive to the underlying lattice structure. We explore suitable settings for the experimental confirmation of these findings.

  1 citation