Publications

Order by: publication date number of citations

• Non-invertible higher-categorical symmetries

  Lakshya Bhardwaj, Lea E. Bottini, Sakura Schäfer-Nameki, Apoorv Tiwari

  SciPost Phys. 14, 007 (2023) · published 26 January 2023 | Toggle abstract · pdf

  We sketch a procedure to capture general non-invertible symmetries of a $d$-dimensional quantum field theory in the data of a higher-category, which captures the local properties of topological defects associated to the symmetries. We also discuss fusions of topological defects, which involve condensations/gaugings of higher-categorical symmetries localized on the worldvolumes of topological defects. Recently some fusions of topological defects were discussed in the literature where the dimension of topological defects seems to jump under fusion. This is not possible in the standard description of higher-categories. We explain that the dimension-changing fusions are understood as higher-morphisms of the higher-category describing the symmetry. We also discuss how a 0-form sub-symmetry of a higher-categorical symmetry can be gauged and describe the higher-categorical symmetry of the theory obtained after gauging. This provides a procedure for constructing non-invertible higher-categorical symmetries starting from invertible higher-form or higher-group symmetries and gauging a 0-form symmetry. We illustrate this procedure by constructing non-invertible 2-categorical symmetries in 4d gauge theories and non-invertible 3-categorical symmetries in 5d and 6d theories. We check some of the results obtained using our approach against the results obtained using a recently proposed approach based on 't Hooft anomalies.

  68 citations

• On the generality of symmetry breaking and dissipative freezing in quantum trajectories

  Joseph Tindall, Dieter Jaksch, Carlos Sánchez Muñoz

  SciPost Phys. Core 6, 004 (2023) · published 25 January 2023 | Toggle abstract · pdf

  Recently, several studies involving open quantum systems which possess a strong symmetry have observed that every individual trajectory in the Monte Carlo unravelling of the master equation will dynamically select a specific symmetry sector to 'freeze' into in the long-time limit. This phenomenon has been termed 'dissipative freezing', and in this paper we argue, by presenting several simple mathematical perspectives on the problem, that it is a general consequence of the presence of a strong symmetry in an open system with only a few exceptions. Using a number of example systems we illustrate these arguments, uncovering an explicit relationship between the spectral properties of the Liouvillian in off-diagonal symmetry sectors and the time it takes for freezing to occur. In the limiting case that eigenmodes with purely imaginary eigenvalues are manifest in these sectors, freezing fails to occur. Such modes indicate the preservation of information and coherences between symmetry sectors of the system and can lead to phenomena such as non-stationarity and synchronisation. The absence of freezing at the level of a single quantum trajectory provides a simple, computationally efficient way of identifying these traceless modes.

  2 citations

• Magnetic impurity in a one-dimensional few-fermion system

  Lukas Rammelmüller, David Huber, Matija Čufar, Joachim Brand, Hans-Werner Hammer, Artem G. Volosniev

  SciPost Phys. 14, 006 (2023) · published 24 January 2023 | Toggle abstract · pdf

  We present a numerical analysis of spin-$\tfrac{1}{2}$ fermions in a one-dimensional harmonic potential in the presence of a magnetic point-like impurity at the center of the trap. The model represents a few-body analogue of a magnetic impurity in the vicinity of an $s$-wave superconductor. Already for a few particles we find a ground-state level crossing between sectors with different fermion parities. We interpret this crossing as a few-body precursor of a quantum phase transition, which occurs when the impurity "breaks" a Cooper pair. This picture is further corroborated by analyzing density-density correlations in momentum space. Finally, we discuss how the system may be realized with existing cold-atoms platforms.

  6 citations

• Nonlocal field theory of quasiparticle scattering in dipolar Bose-Einstein condensates

  Caio C. Holanda Ribeiro, Uwe R. Fischer

  SciPost Phys. Core 6, 003 (2023) · published 23 January 2023 | Toggle abstract · pdf

  We consider the propagation of quasiparticle excitations in a dipolar Bose-Einstein condensate, and derive a nonlocal field theory of quasiparticle scattering at a stepwise inhomogeneity of the sound speed, obtained by tuning the contact coupling part of the interaction on one side of the barrier. To solve this problem ab initio, i.e., without prior assumptions on the form of the solutions, we reformulate the dipolar Bogoliubov-de Gennes equation as a singular integral equation. The latter is of a novel hypersingular type, in having a kernel which is hypersingular at only two isolated points. Deriving its solution, we show that the integral equation reveals a continuum of evanescent channels at the sound barrier which is absent for a purely contact-interaction condensate. We furthermore demonstrate that by performing a discrete approximation for the kernel, one achieves an excellent solution accuracy for already a moderate number of discretization steps. Finally, we show that the non-monotonic nature of the system dispersion, corresponding to the emergence of a roton minimum in the excitation spectrum, results in peculiar features of the transmission and reflection at the sound barrier which are nonexistent for contact interactions.

  1 citation

• A comprehensive study of the velocity, momentum and position matrix elements for Bloch states: Application to a local orbital basis

  Juan José Esteve-Paredes, Juan José Palacios

  SciPost Phys. Core 6, 002 (2023) · published 20 January 2023 | Toggle abstract · pdf

  We present a comprehensive study of the velocity operator, $\hat{\boldsymbol{v}}=\frac{i}{\hbar} [\hat{H},\hat{\boldsymbol{r}}]\,$, when used in crystalline solids calculations. The velocity operator is key to the evaluation of a number of physical properties and its computation, both from a practical and fundamental perspective, has been a long-standing debate for decades. Our work summarizes the different approaches found in the literature, but never connected before in a comprehensive manner. In particular we show how one can compute the velocity matrix elements following two different routes. One where the commutator is explicitly used and another one where the commutator is avoided by relying on the Berry connection. We work out an expression in the latter scheme to compute velocity matrix elements, generalizing previous results. In addition, we show how this procedure avoids ambiguous mathematical steps and how to properly deal with the two popular gauge choices that coexist in the literature. As an illustration of all this, we present several examples using tight-binding models and local density functional theory calculations, in particular using Gaussian-type localized orbitals as basis sets. We show how the the velocity operator cannot be approximated, in general, by the $k$-gradient of the Bloch Hamiltonian matrix when a non-orthonormal basis set is used. Finally, we also compare with its real-space evaluation through the identification with the canonical momentum operator when possible. This comparison offers us, in addition, a glimpse of the importance of non-local corrections, which may invalidate the naive momentum-velocity correspondence.

  6 citations

• Unsupervised and supervised learning of interacting topological phases from single-particle correlation functions

  Simone Tibaldi, Giuseppe Magnifico, Davide Vodola, Elisa Ercolessi

  SciPost Phys. 14, 005 (2023) · published 19 January 2023 | Toggle abstract · pdf

  The recent advances in machine learning algorithms have boosted the application of these techniques to the field of condensed matter physics, in order e.g. to classify the phases of matter at equilibrium or to predict the real-time dynamics of a large class of physical models. Typically in these works, a machine learning algorithm is trained and tested on data coming from the same physical model. Here we demonstrate that unsupervised and supervised machine learning techniques are able to predict phases of a non-exactly solvable model when trained on data of a solvable model. In particular, we employ a training set made by single-particle correlation functions of a non-interacting quantum wire and by using principal component analysis, k-means clustering, t-distributed stochastic neighbor embedding and convolutional neural networks we reconstruct the phase diagram of an interacting superconductor. We show that both the principal component analysis and the convolutional neural networks trained on the data of the non-interacting model can identify the topological phases of the interacting model. Our findings indicate that non-trivial phases of matter emerging from the presence of interactions can be identified by means of unsupervised and supervised techniques applied to data of non-interacting systems.

  14 citations

• Time-reparametrization invariances, multithermalization and the Parisi scheme

  Jorge Kurchan

  SciPost Phys. Core 6, 001 (2023) · published 17 January 2023 | Toggle abstract · pdf

  The Parisi scheme for equilibrium and the corresponding slow dynamics with multithermalization - same temperature common to all observables, different temperatures only possible at widely separated timescales – imply one another. Consistency requires that two systems brought into infinitesimal coupling be able to rearrange their timescales in order that all their temperatures match: this time reorganisation is only possible because the systems have a set of time-reparametrization invariances, that are thus seen to be an essential component of the scenario.

  2 citations

• Quantum order-by-disorder induced phase transition in Rydberg ladders with staggered detuning

  Madhumita Sarkar, Mainak Pal, Arnab Sen, Krishnendu Sengupta

  SciPost Phys. 14, 004 (2023) · published 16 January 2023 | Toggle abstract · pdf

  $^{87}{\rm Rb}$ atoms are known to have long-lived Rydberg excited states with controllable excitation amplitude (detuning) and strong repulsive van der Waals interaction $V_{{\bf r} {\bf r'}}$ between excited atoms at sites ${\bf r}$ and ${\bf r'}$. Here we study such atoms in a two-leg ladder geometry in the presence of both staggered and uniform detuning with amplitudes $\Delta$ and $\lambda$ respectively. We show that when $V_{{\bf r r'}} \gg(\ll) \Delta, \lambda$ for $|{\bf r}-{\bf r'}|=1(>1)$, these ladders host a plateau for a wide range of $\lambda/\Delta$ where the ground states are selected by a quantum order-by-disorder mechanism from a macroscopically degenerate manifold of Fock states with fixed Rydberg excitation density $1/4$. Our study further unravels the presence of an emergent Ising transition stabilized via the order-by-disorder mechanism inside the plateau. We identify the competing terms responsible for the transition and estimate a critical detuning $\lambda_c/\Delta=1/3$ which agrees well with exact-diagonalization based numerical studies. We also study the fate of this transition for a realistic interaction potential $V_{{\bf r} {\bf r'}} = V_0 /|{\bf r}-{\bf r'}|^6$, demonstrate that it survives for a wide range of $V_0$, and provide analytic estimate of $\lambda_c$ as a function of $V_0$. This allows for the possibility of a direct verification of this transition in standard experiments which we discuss.

  3 citations

• Pauli crystal melting in shaken optical traps

  Jiabing Xiang, Paolo Molignini, Miriam Büttner, Axel U. J. Lode

  SciPost Phys. 14, 003 (2023) · published 13 January 2023 | Toggle abstract · pdf

  Pauli crystals are ordered geometric structures that emerge in trapped noninteracting fermionic systems due to their underlying Pauli repulsion. The deformation of Pauli crystals - often called melting - has been recently observed in experiments, but the mechanism that leads to it remains unclear. We address this question by studying the melting dynamics of $N=6$ fermions as a function of periodic driving and experimental imperfections in the trap (anisotropy and anharmonicity) by employing a combination of numerical simulations and Floquet theory. Surprisingly, we reveal that the melting of Pauli crystals is not simply a direct consequence of an increase in system energy, but is instead related to the trap geometry and the population of the Floquet modes. We show that the melting is absent in traps without imperfections and triggered only by a sufficiently large shaking amplitude in traps with imperfections.

  1 citation

• Effective fractonic behavior in a two-dimensional exactly solvable spin liquid

  Guilherme Delfino, Weslei Bernardino Fontana, Pedro R. S. Gomes, Claudio Chamon

  SciPost Phys. 14, 002 (2023) · published 12 January 2023 | Toggle abstract · pdf

  In this work we propose a $\mathbb{Z}_N$ clock model which is exactly solvable on the lattice. We find exotic properties for the low-energy physics, such as UV/IR mixing and excitations with restricted mobility, that resemble fractonic physics from higher dimensional models. We then study the continuum descriptions for the lattice system in two distinct regimes and find two qualitative distinct field theories for each one of them. A characteristic time scale that grows exponentially fast with $N^2$ (and diverges rapidly as function of system parameters) separates these two regimes. For times below this scale, the system is described by an effective fractonic Chern-Simons-like action, where higher-form symmetries prevent quasiparticles from hopping. In this regime, the system behaves effectively as a fracton as isolated particles, in practice, never leave their original position. Beyond the large characteristic time scale, the excitations are mobile and the effective field theory is given by a pure mutual Chern-Simons action. In this regime, the UV/IR properties of the system is captured by a peculiar realization of the translation group.

  8 citations