Publications

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• x-y duality in topological recursion for exponential variables via quantum dilogarithm

  Alexander Hock

  SciPost Phys. 17, 065 (2024) · published 23 August 2024 | Toggle abstract · pdf

  For a given spectral curve, the theory of topological recursion generates two different families $\omega_{g,n}$ and $\omega_{g,n}^\vee$ of multi-differentials, which are for algebraic spectral curves related via the universal $x-y$ duality formula. We propose a formalism to extend the validity of the $x-y$ duality formula of topological recursion from algebraic curves to spectral curves with exponential variables of the form $e^x=F(e^y)$ or $e^x=F(y)e^{a y}$ with $F$ rational and $a$ some complex number, which was in principle already observed in [Commun. Number Theory Phys. 13, 763 (2019); J. Lond. Math. Soc. 109, e12946 (2024)]. From topological recursion perspective the family $\omega_{g,n}^\vee$ would be trivial for these curves. However, we propose changing the $n=1$ sector of $\omega_{g,n}^\vee$ via a version of the Faddeev's quantum dilogarithm which will lead to the correct two families $\omega_{g,n}$ and $\omega_{g,n}^\vee$ related by the same $x-y$ duality formula as for algebraic curves. As a consequence, the $x-y$ symplectic transformation formula extends further to important examples governed by topological recursion including, for instance, Gromov-Witten invariants of $\mathbb{C}^3$ (or, equivalently, triple Hodge integrals), orbifold Hurwitz numbers, and stationary Gromov-Witten invariants of $\mathbb{P}^1$. The proposed formalism is related to the issue topological recursion encounters for specific choices of framings for the topological vertex curve.

  1 citation

• Phase transitions of wave packet dynamics in disordered non-Hermitian systems

  Helene Spring, Viktor Könye, Fabian A. Gerritsma, Ion Cosma Fulga, Anton R. Akhmerov

  SciPost Phys. 16, 120 (2024) · published 3 May 2024 | Toggle abstract · pdf

  Disorder can localize the eigenstates of one-dimensional non-Hermitian systems, leading to an Anderson transition with a critical exponent of 1. We show that, due to the lack of energy conservation, the dynamics of individual, real-space wave packets follows a different behavior. Both transitions between localization and unidirectional amplification, as well as transitions between distinct propagating phases become possible. The critical exponent of the transition is close to 1/2 in propagating-propagating and (de)localization transitions.

  1 citation

• Traveling discontinuity at the quantum butterfly front

  Camille Aron, Éric Brunet, Aditi Mitra

  SciPost Phys. 15, 042 (2023) · published 2 August 2023 | Toggle abstract · pdf

  We formulate a kinetic theory of quantum information scrambling in the context of a paradigmatic model of interacting electrons in the vicinity of a superconducting phase transition. We carefully derive a set of coupled partial differential equations that effectively govern the dynamics of information spreading in generic dimensions. Their solutions show that scrambling propagates at the maximal speed set by the Fermi velocity. At early times, we find exponential growth at a rate set by the inelastic scattering. At late times, we find that scrambling is governed by shock-wave dynamics with traveling waves exhibiting a discontinuity at the boundary of the light cone. Notably, we find perfectly causal dynamics where the solutions do not spill outside of the light cone.

  1 citation

• Electric polarization and magnetization in metals

  Perry T. Mahon, John E. Sipe

  SciPost Phys. 14, 058 (2023) · published 3 April 2023 | Toggle abstract · pdf

  A feature of the "modern theory" is that electric polarization is not well-defined in a metallic ground state. A different approach invokes the general existence of a complete set of exponentially localized Wannier functions, with respect to which general definitions of microscopic electronic polarization and magnetization fields, and free charge and current densities are always admitted. These definitions assume no particular initial electronic state of the crystal, and the set of microscopic fields satisfy the usual relations of classical electrodynamics. Notably, when applied to a trivial insulator initially occupying its $T=0$ ground state, the expressions for the unperturbed polarization and orbital magnetization, and for the orbital magnetoelectric polarizability tensor obtained from these different approaches can agree. However, the "modern theory of magnetization" has been extended via thermodynamic arguments to include metals and Chern insulators. We here compare with that generalization and find disagreement; the manner in which the expressions differ elucidates the distinct philosophies of these approaches. Our approach leads to the usual electrical conductivity tensor in the long-wavelength limit; in the absence of any scattering mechanisms, the dc divergence of that tensor is due to the free current density and the finite-frequency generalization of the anomalous Hall contribution arises from a combination of bound and free current densities. As well, in the limit that the electronic ground state is that of a trivial insulator, our expressions reduce to those expected for the unperturbed polarization and magnetization, and the electric susceptibility.

  1 citation

• A path integral ground state Monte Carlo algorithm for entanglement of lattice bosons

  Emanuel Casiano-Diaz, C. M. Herdman, Adrian Del Maestro

  SciPost Phys. 14, 054 (2023) · published 29 March 2023 | Toggle abstract · pdf

  A ground state path integral quantum Monte Carlo algorithm is introduced that allows for the study of entanglement in lattice bosons at zero temperature. The Rényi entanglement entropy between spatial subregions is explored across the phase diagram of the one dimensional Bose-Hubbard model for systems consisting of up to $L=256$ sites at unit-filling without any restrictions on site occupancy, far beyond the reach of exact diagonalization. The favorable scaling of the algorithm is demonstrated through a further measurement of the Rényi entanglement entropy at the two dimensional superfluid-insulator critical point for large system sizes, confirming the existence of the expected entanglement boundary law in the ground state. The Rényi estimator is extended to measure the symmetry resolved entanglement that is operationally accessible as a resource for experimentally relevant lattice gases with fixed total particle number.

  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

• Quantum oscillations in an impurity-band Anderson insulator

  Nigel R. Cooper, Jack Kelsall

  SciPost Phys. 15, 118 (2023) · published 27 September 2023 | Toggle abstract · pdf

  We show that for a system of localized electrons in an impurity band, which form an Anderson insulating state at zero temperature, there can appear quantum oscillations of the magnetization, i.e. the Anderson insulator can exhibit the de Haas-van Alphen effect. This is possible when the electronic band from which the localized states are formed has an extremum that traces out a nonzero area in reciprocal space. Our work extends existing theories for clean band insulators of this form to the situation where they host an impurity band. We show that the energies of these impurity levels oscillate with magnetic field, and compute the conditions under which these oscillations can dominate the de Haas-van Alphen effect. We discuss our results in connection with experimental measurements of quantum oscillations in Kondo insulators, and propose other experimental systems where the impurity band contribution can be dominant.

  1 citation

• Probing black hole microstate evolution with networks and random walks

  Anthony M. Charles, Daniel R. Mayerson

  SciPost Phys. 8, 077 (2020) · published 14 May 2020 | Toggle abstract · pdf

  We model black hole microstates and quantum tunneling transitions between them with networks and simulate their time evolution using well-established tools in network theory. In particular, we consider two models based on Bena-Warner three-charge multi-centered microstates and one model based on the D1-D5 system; we use network theory methods to determine how many centers (or D1-D5 string strands) we expect to see in a typical late-time state. We find three distinct possible phases in parameter space for the late-time behaviour of these networks, which we call ergodic, trapped, and amplified, depending on the relative importance and connectedness of microstates. We analyze in detail how these different phases of late-time behavior are related to the underlying physics of the black hole microstates. Our results indicate that the expected properties of microstates at late times cannot always be determined simply by entropic arguments; typicality is instead a highly non-trivial, emergent property of the full Hilbert space of microstates.

  1 citation

• Disordered non-Fermi liquid fixed point for two-dimensional metals at Ising-nematic quantum critical points

  Kyoung-Min Kim, Ki-Seok Kim

  SciPost Phys. 17, 059 (2024) · published 23 August 2024 | Toggle abstract · pdf

  Understanding the influence of quenched random potential is crucial for comprehending the exotic electronic transport of non-Fermi liquid metals near metallic quantum critical points. In this study, we identify a stable fixed point governing the quantum critical behavior of two-dimensional non-Fermi liquid metals in the presence of a random potential disorder. By performing renormalization group analysis on a dimensional-regularized field theory for Ising-nematic quantum critical points, we systematically investigate the interplay between random potential disorder for electrons and Yukawa-type interactions between electrons and bosonic order-parameter fluctuations in a perturbative epsilon expansion. At the one-loop order, the effective field theory lacks stable fixed points, instead exhibiting a runaway flow toward infinite disorder strength. However, at the two-loop order, the effective field theory converges to a stable fixed point characterized by finite disorder strength, termed the "disordered non-Fermi liquid (DNFL) fixed point". Our investigation reveals that two-loop vertex corrections induced by Yukawa couplings are pivotal in the emergence of the DNFL fixed point, primarily through screening disorder scattering. Additionally, the DNFL fixed point is distinguished by a substantial anomalous scaling dimension of fermion fields, resulting in pseudogap-like behavior in the electron's density of states. These findings shed light on the quantum critical behavior of disordered non-Fermi liquid metals, emphasizing the indispensable role of higher-order loop corrections in such comprehension.

  1 citation

• Effective field theory of fluctuating wall in open systems: from a kink in Josephson junction to general domain wall

  Keisuke Fujii, Masaru Hongo

  SciPost Phys. 12, 160 (2022) · published 13 May 2022 | Toggle abstract · pdf

  We investigate macroscopic behaviors of fluctuating domain walls in nonequilibrium open systems with the help of the effective field theory based on symmetry. Since the domain wall in open systems breaks the translational symmetry, there appears a gapless excitation identified as the Nambu-Goldstone (NG) mode, which shows the non-propagating diffusive behavior in contrast to those in closed systems. After demonstrating the presence of the diffusive NG mode in the $(2+1)$-dimensional dissipative Josephson junction, we provide a symmetry-based general analysis for open systems breaking the one-dimensional translational symmetry. A general effective Lagrangian is constructed based on the Schwinger-Keldysh formalism, which supports the presence of the gapless diffusion mode in the fluctuation spectrum in the thin wall regime. Besides, we also identify a term peculiar to the open system, which possibly leads to the instability in the thick-wall regime or the nonlinear Kardar-Parisi-Zhang coupling in the thin-wall regime although it is absent in the Josephson junction.

  1 citation