Publications

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Cavity-induced bifurcation in classical rate theory

Kalle Sulo Ukko Kansanen, Tero Tapio Heikkilä

SciPost Phys. 16, 025 (2024) · published 23 January 2024 | · pdf

We show how coupling an ensemble of bistable systems to a common cavity field affects the collective stochastic behavior of this ensemble. In particular, the cavity provides an effective interaction between the systems, and parametrically modifies the transition rates between the metastable states. We predict that the cavity induces a phase transition at a critical temperature which depends linearly on the number of systems. It shows up as a spontaneous symmetry breaking where the stationary states of the bistable system bifurcate. We observe that the transition rates slow down independently of the phase transition, but the rate modification vanishes for alternating signs of the system-cavity couplings, corresponding to a disordered ensemble of dipoles. Our results are of particular relevance in polaritonic chemistry where the presence of a cavity has been suggested to affect chemical reactions.
Topological-insulator nanocylinders

Michele Governale, Fabio Taddei

SciPost Phys. Core 6, 032 (2023) · published 21 April 2023 | · pdf

Nanostructures, such a quantum dots or nanoparticles, made of three-dimensional topological insulators (3DTIs) have been recently attracting increasing interest, especially for their optical properties. In this paper we calculate the energy spectrum, the surface states and the dipole matrix elements for optical transitions with in-plane polarization of 3DTI nanocylinders of finite height $L$ and radius $R$. We first derive an effective 2D Hamiltonian by exploiting the cylindrical symmetry of the problem. We develop two approaches: the first one is an exact numerical tight-binding model obtained by discretising the Hamiltonian. The second one, which allows us to obtain analytical results, is an approximated model based on a large-$R$ expansion and on an effective boundary condition to account for the finite height of the nanocylinder. We find that the agreement between the two models, as far as eigenenergies and eigenfunctions are concerned, is excellent for the lowest absolute value of the longitudinal component of the angular momentum. Finally, we derive analytical expressions for the dipole matrix elements by first considering the lateral surface alone and the bases alone, and then for the whole nanocylinder. In particular, we focus on the two limiting cases of tall and squat nanocylinders. The latter case is compared with the numerical results finding a good agreement.
Mean-field theory of first-order quantum superconductor-insulator transition

Igor Poboiko, Mikhail Feigel'man

SciPost Phys. 17, 066 (2024) · published 23 August 2024 | · pdf

Recent experimental studies on strongly disordered indium oxide films have revealed an unusual first-order quantum phase transition between the superconducting and insulating states (SIT). This transition is characterized by a discontinuous jump from non-zero to zero values of superfluid stiffness at the critical point, contradicting the conventional "scaling scenario" typically associated with SIT. In this paper, we present a theoretical framework for understanding this first-order transition. Our approach is based on the concept of competition between two fundamentally distinct ground states that arise from electron pairs initially localized by strong disorder: the superconducting state and the Coulomb glass insulator. These ground states are distinguished by two crucially different order parameters, suggesting a natural expectation of a discontinuous transition between them at $T=0$. This transition occurs when the magnitudes of the superconducting gap $\Delta$ and the Coulomb gap $E_C$ become comparable. Additionally, we extend our analysis to low non-zero temperatures and provide a mean-field "phase diagram" in the plane of $(T/\Delta,E_C/\Delta)$. Our results reveal the existence of a natural upper bound for the kinetic inductance of strongly disordered superconductors.
Anti-holomorphic modes in vortex lattices

Brook J. Hocking, Thomas Machon

SciPost Phys. 14, 080 (2023) · published 24 April 2023 | · pdf

A continuum theory of linearized Helmholtz-Kirchoff point vortex dynamics about a steadily rotating lattice state is developed by two separate methods: firstly by a direct procedure, secondly by taking the long-wavelength limit of Tkachenko's exact solution for a triangular vortex lattice. Solutions to the continuum theory are found, described by arbitrary anti-holomorphic functions, and give power-law localized edge modes. Numerical results for finite lattices show excellent agreement to the theory.
On perturbation around closed exclusion processes

Masataka Watanabe

SciPost Phys. 17, 092 (2024) · published 25 September 2024 | · pdf

We derive the formula for the stationary states of particle-number conserving exclusion processes infinitesimally perturbed by inhomogeneous adsorption and desorption. The formula not only proves but also generalises the conjecture proposed in [Phys. Rev. E 97, 032135] to account for inhomogeneous adsorption and desorption. As an application of the formula, we draw part of the phase diagrams of the open asymmetric simple exclusion process with and without Langmuir kinetics, correctly reproducing known results.
A linear algebra-based approach to understanding the relation between the winding number and zero-energy edge states

Chen-Shen Lee

SciPost Phys. Core 7, 003 (2024) · published 30 January 2024 | · pdf

The one-to-one relation between the winding number and the number of robust zero-energy edge states, known as bulk-boundary correspondence, is a celebrated feature of 1$d$ systems with chiral symmetry. Although this property can be explained by the K-theory, the underlying mechanism remains elusive. Here, we demonstrate that, even without resorting to advanced mathematical techniques, one can prove this correspondence and clearly illustrate the mechanism using only Cauchy's integral and elementary algebra. Furthermore, our approach to proving bulk-boundary correspondence also provides clear insights into a kind of system that doesn't respect chiral symmetry but can have robust left or right zero-energy edge states. In such systems, one can still assign the winding number to characterize these zero-energy edge states.
Catalogue of phonon modes in several cuprate high-temperature superconductors from density functional theory

Noah J. Jabusch, Pavan Dayal, Alexander F. Kemper

SciPost Phys. Core 6, 018 (2023) · published 23 March 2023 | · pdf

Cuprates are promising candidates for study in developing higher temperature superconductors. A thorough understanding of a material's phonon modes enables further investigation of its emergent properties, however, no complete reference of the phonon modes exists. Here, using density functional theory, we evaluate the phonon frequencies and atomic displacements for $\text{La}_2\text{CuO}_4$, $\text{Bi}_2\text{Sr}_2\text{CuO}_6$, and $\text{Bi}_2\text{Sr}_2\text{CaCu}_2\text{O}_8$, in their tetragonal structures. The phonon modes for all materials agree with those expected from space group symmetry and display instabilities corresponding to known low-temperature structural phase transitions.
Higgs-confinement transitions in QCD from symmetry protected topological phases

Thomas T. Dumitrescu, Po-Shen Hsin

SciPost Phys. 17, 093 (2024) · published 26 September 2024 | · pdf

In gauge theories with fundamental matter there is typically no sharp way to distinguish confining and Higgs regimes, e.g. using generalized global symmetries acting on loop order parameters. It is standard lore that these two regimes are continuously connected, as has been explicitly demonstrated in certain lattice and continuum models. We point out that Higgsing and confinement sometimes lead to distinct symmetry protected topological (SPT) phases -- necessarily separated by a phase transition -- for ordinary global symmetries. We present explicit examples in 3+1 dimensions, obtained by adding elementary Higgs fields and Yukawa couplings to QCD while preserving parity $\mathsf{P}$ and time reversal $\mathsf{T}$. In a suitable scheme, the confining phases of these theories are trivial SPTs, while their Higgs phases are characterized by non-trivial $\mathsf{P}$- and $\mathsf{T}$-invariant theta-angles $\theta_f, \theta_g = \pi$ for flavor or gravity background gauge fields, i.e. they are topological insulators or superconductors. Finally, we consider conventional three-flavor QCD (without elementary Higgs fields) at finite $U(1)_B$ baryon-number chemical potential $\mu_B$, which preserves $\mathsf{P}$ and $\mathsf{T}$. At very large $\mu_B$, three-flavor QCD is known to be a completely Higgsed color superconductor that also spontaneously breaks $U(1)_B$. We argue that this high-density phase is in fact a gapless SPT, with a gravitational theta-angle $\theta_g = \pi$ that safely co-exists with the $U(1)_B$ Nambu-Goldstone boson. We explain why this SPT motivates unexpected transitions in the QCD phase diagram, as well as anomalous surface modes at the boundary of quark-matter cores inside neutron stars.
Spatial separation of spin currents in transition metal dichalcogenides

Antonio L. R. Manesco, Artem Pulkin

SciPost Phys. Core 6, 036 (2023) · published 1 May 2023 | · pdf

We theoretically predict spatial separation of spin-polarized ballistic currents in transition metal dichalcogenides (TMDs) due to trigonal warping. We quantify the effect in terms of spin polarization of charge carrier currents in a prototypical 3-terminal ballistic device where spin-up and spin-down charge carriers are collected by different leads. We show that the magnitude of the current spin polarization depends strongly on the charge carrier energy and the direction with respect to crystallographic orientations in the device. We study the (negative) effect of lattice imperfections and disorder on the observed spin polarization. Our investigation provides an avenue towards observing spin discrimination in a defect-free time reversal-invariant material.
Real-space spectral simulation of quantum spin models: Application to generalized Kitaev models

Francisco M. O. Brito, Aires Ferreira

SciPost Phys. Core 7, 006 (2024) · published 21 February 2024 | · pdf

The proliferation of quantum fluctuations and long-range entanglement presents an outstanding challenge for the numerical simulation of interacting spin systems with exotic ground states. Here, we present a toolset of Chebyshev polynomial-based iterative methods that provides a unified framework to study the thermodynamical properties, critical behavior and dynamics of frustrated quantum spin models with controlled accuracy. Similar to previous applications of the Chebyshev spectral methods to condensed matter systems, the algorithmic complexity scales linearly with the Hilbert space dimension and the Chebyshev truncation order. Using this approach, we study two paradigmatic quantum spin models on the honeycomb lattice: the Kitaev-Heisenberg (K-H) and the Kitaev-Ising (K-I) models. We start by applying the Chebyshev toolset to compute nearest-neighbor spin correlations, specific heat and entropy of the K-H model on a 24-spin cluster. Our results are benchmarked against exact diagonalization and a popular iterative method based on thermal pure quantum states. The transitions between a variety of magnetic phases, namely ferromagnetic, Néel, zigzag and stripy antiferromagnetic and quantum spin liquid phases are obtained accurately and efficiently. We also determine the temperature dependence of the spin correlations, over more than three decades in temperature, by means of a finite temperature Chebyshev polynomial method introduced here. Finally, we report novel dynamical signatures of the quantum phase transitions in the K-I model. Our findings suggest that the efficiency, versatility and low-temperature stability of the Chebyshev framework developed here could pave the way for previously unattainable studies of quantum spin models in two dimensions.

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