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.

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.

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.

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.

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.