Publications

Order by: publication date number of citations

• Concentration of quantum equilibration and an estimate of the recurrence time

  Jonathon Riddell, Nathan J. Pagliaroli, Álvaro M. Alhambra

  SciPost Phys. 15, 165 (2023) · published 16 October 2023 | Toggle abstract · pdf

  We show that the dynamics of generic quantum systems concentrate around their equilibrium value when measuring at arbitrary times. This means that the probability of finding such values away from that equilibrium is exponentially suppressed, with a decay rate given by the effective dimension. Our result allows us to place a lower bound on the recurrence time of quantum systems, since recurrences corresponds to the rare events of finding a state away from equilibrium. In many-body systems, this bound is doubly exponential in system size. We also show corresponding results for free fermions, which display a weaker concentration and earlier recurrences.

• Lifting integrable models and long-range interactions

  Marius de Leeuw, Ana Lucia Retore

  SciPost Phys. 15, 241 (2023) · published 15 December 2023 | Toggle abstract · pdf

  In this paper we discuss a constructive approach to check whether a constant Hamiltonian is Yang-Baxter integrable. We then apply our method to long-range interactions and find the Lax operator and R-matrix of the three-loop SU(2) sector in N=4 SYM. We show that all known integrable long-range deformations of the 6-vertex models of this type can be obtained from a Lax operator and an R-matrix. Finally we discuss what happens at higher loops and highlight some general structures that these models exhibit.

• A numerical study of bounds in the correlations of fractional quantum Hall states

  Prashant Kumar, Frederick Duncan Michael Haldane

  SciPost Phys. 16, 117 (2024) · published 1 May 2024 | Toggle abstract · pdf

  We numerically compute the guiding center static structure factor $\bar S(k)$ of various fractional quantum Hall (FQH) states to $\mathcal{O}(k\ell)^6$ where $k$ is the wavenumber and $\ell$ is the magnetic length. Employing density matrix renormalization group on an infinite cylinder of circumference $L_y$, we study the two-dimensional limit using $L_y/\xi \gg 1$, where $\xi$ is the correlation length. The main findings of our work are: 1) the ground states that deviate away from the ideal conformal block wavefunctions, do not saturate the Haldane bound, and 2) the coefficient of $O(k\ell)^6$ term appears to be bounded above by a value predicted by field theories proposed in the literature. The first finding implies that the graviton mode is not maximally chiral for experimentally relevant FQH states.

• Gravitational multipoles in general stationary spacetimes

  Daniel R. Mayerson

  SciPost Phys. 15, 154 (2023) · published 11 October 2023 | Toggle abstract · pdf

  The Geroch-Hansen and Thorne (ACMC) formalisms give rigorous and equivalent definitions for gravitational multipoles in stationary vacuum spacetimes. However, despite their ubiquitous use in gravitational physics, it has not been shown that these formalisms can be generalized to non-vacuum stationary solutions, except in a few special cases. This paper shows how the Geroch-Hansen formalism can be generalized to arbitrary non-vacuum stationary spacetimes for metrics that are sufficiently smooth at infinity. The key is the construction of an improved twist vector, which is well-defined under a mild topological condition on the spacetime (which is automatically satisfied for black holes). Ambiguities in the construction of this improved twist vector are discussed and fixed by imposing natural "gauge fixing" conditions, which also immediately lead to the equivalence between the Geroch-Hansen and Thorne formalisms for such arbitrary stationary spacetimes.

• Universal Chern number statistics in random matrix fields

  Or Swartzberg, Michael Wilkinson, Omri Gat

  SciPost Phys. 15, 015 (2023) · published 19 July 2023 | Toggle abstract · pdf

  We investigate the probability distribution of Chern numbers (quantum Hall conductance integers) for a parametric version of the GUE random matrix ensemble, which is a model for a chaotic or disordered system. The numerically-calculated single-band Chern number statistics agree well with predictions based on an earlier study [O. Gat and M. Wilkinson, SciPost Phys., 10, 149, (2021)] of the statistics of the quantum adiabatic curvature, when the parametric correlation length is small. However, contrary to an earlier conjecture, we find that the gap Chern numbers are correlated, and that the correlation is weak but slowly-decaying. Also, the statistics of weighted sums of Chern numbers differs markedly from predictions based upon the hypothesis that gap Chern numbers are uncorrelated. All our results are consistent with the universality hypothesis described in the earlier paper, including in the previously unstudied regime of large correlation length, where the Chern statistics is highly non-Gaussian.

• On non-canonical degrees of freedom

  Eoin Quinn

  SciPost Phys. 10, 075 (2021) · published 25 March 2021 | Toggle abstract · pdf

  Non-canonical degrees of freedom provide one of the most promising routes towards characterising a range of important phenomena in condensed matter physics. Potential candidates include the pseudogap regime of the cuprates, heavy-fermion behaviour, and also indeed magnetically ordered systems. Nevertheless it remains an open question whether non-canonical algebras can in fact provide legitimate quantum degrees of freedom. In this paper we survey progress made on this topic, complementing distinct approaches so as to obtain a unified description. In particular we obtain a novel exact representation for a self-energy-like object for non-canonical degrees of freedom. We further make a resummation of density correlations to obtain analogues of the RPA and GW approximations commonly employed for canonical degrees of freedom. We discuss difficulties related to generating higher-order approximations which are consistent with conservation laws, which represents an outstanding issue. We also discuss how the interplay between canonical and non-canonical degrees of freedom offers a useful paradigm for organising the phase diagram of correlated electronic behaviour.

• Monopoles in Dirac spin liquids and their symmetries from instanton calculus

  Shankar Ganesh, Joseph Maciejko

  SciPost Phys. 16, 118 (2024) · published 2 May 2024 | Toggle abstract · pdf

  The Dirac spin liquid (DSL) is a two-dimensional (2D) fractionalized Mott insulator featuring massless Dirac spinon excitations coupled to a compact U(1) gauge field, which allows for flux-tunneling instanton events described by magnetic monopoles in (2+1)D Euclidean spacetime. The state-operator correspondence of conformal field theory has been used recently to define associated monopole operators and determine their quantum numbers, which encode the microscopic symmetries of conventional ordered phases proximate to the DSL. In this work, we utilize semiclassical instanton methods not relying on conformal invariance to construct monopole operators directly in (2+1)D spacetime as instanton-induced 't Hooft vertices, i.e., fermion-number-violating effective interactions originating from zero modes of the Euclidean Dirac operator in an instanton background. In the presence of a flavor-adjoint fermion mass, resummation of the instanton gas is shown to select the correct monopole to be proliferated, in accordance with predictions of the state-operator correspondence. We also show that our instanton-based approach is able to determine monopole quantum numbers on bipartite lattices.

• One-form symmetries in $\mathcal{N} = 3$ S-folds

  Antonio Amariti, Davide Morgante, Antoine Pasternak, Simone Rota, Valdo Tatitscheff

  SciPost Phys. 15, 132 (2023) · published 3 October 2023 | Toggle abstract · pdf

  We classify the global one-form symmetries for non-Lagrangian $\mathcal{N}=3$ SCFTs that arise by the action of $S$-fold projections on D3-branes. Such a classification is dictated, on a generic point of the Coulomb branch, by probing the charge spectrum of $(p, q)$-strings in the brane setup. The charge lattice of lines is then obtained by finding the ones that are genuine modulo screening by dynamical particles. The one-form symmetries are then extracted from the maximal sub-lattices of mutually local lines. We further comment on the existence of non-invertible symmetries for some of these $\mathcal{N}=3$ SCFTs.

• Higher-group symmetry of (3+1)D fermionic $\mathbb{Z}_2$ gauge theory: Logical CCZ, CS, and T gates from higher symmetry

  Maissam Barkeshli, Po-Shen Hsin, Ryohei Kobayashi

  SciPost Phys. 16, 122 (2024) · published 7 May 2024 | Toggle abstract · pdf

  It has recently been understood that the complete global symmetry of finite group topological gauge theories contains the structure of a higher-group. Here we study the higher-group structure in (3+1)D $\mathbb{Z}_2$ gauge theory with an emergent fermion, and point out that pumping chiral $p+ip$ topological states gives rise to a $\mathbb{Z}_{8}$ 0-form symmetry with mixed gravitational anomaly. This ordinary symmetry mixes with the other higher symmetries to form a 3-group structure, which we examine in detail. We then show that in the context of stabilizer quantum codes, one can obtain logical CCZ and CS gates by placing the code on a discretization of $T^3$ (3-torus) and $T^2 \rtimes_{C_2} S^1$ (2-torus bundle over the circle) respectively, and pumping $p+ip$ states. Our considerations also imply the possibility of a logical $T$ gate by placing the code on $\mathbb{RP}^3$ and pumping a $p+ip$ topological state.

• Entanglement in the quantum Hall fluid of dipoles

  Jackson R. Fliss

  SciPost Phys. 11, 052 (2021) · published 9 September 2021 | Toggle abstract · pdf

  We revisit a model for gapped fractonic order in (2+1) dimensions (a symmetric-traceless tensor gauge theory with conservation of dipole and trace-quadrupole moments described in \cite{Prem:2017kxc}) and compute its ground-state entanglement entropy on $\mathbb R^2$. Along the way, we quantize the theory on open subsets of $\mathbb R^2$ which gives rise to gapless edge excitations that are Lifshitz-type scalar theories. We additionally explore varieties of gauge-invariant extended operators and rephrase the fractonic physics in terms of the local deformability of these operators. We explore similarities of this model to the effective field theories describing quantum Hall fluids: in particular, quantization of dipole moments through a novel compact symmetry leads us to interpret the vacuum of this theory as a dipole condensate atop of which dipoles with fractionalized moments appear as quasi-particle excitations with Abelian anyonic statistics. This interpretation is reflected in the subleading ``topological entanglement" correction to the entanglement entropy. We extend this result to a series of models with conserved multipole moments.