Publications

Order by: publication date number of citations

• Higher-order topological superconductors from Weyl semimetals

  Ammar Jahin , Apoorv Tiwari , Yuxuan Wang

  SciPost Phys. 12, 053 (2022) · published 4 February 2022 | Toggle abstract · pdf

  We propose that doped Weyl semimetals with {time-reversal and certain crystalline symmetries} are natural candidates to realize higher-order topological superconductors, which exhibit a fully gapped bulk while the surface hosts robust gapless chiral hinge states. We show that in such a doped Weyl semimetal, a featureless finite-range attractive interaction favors a $p+ip$ pairing symmetry. By analyzing its topological properties, we identify such a chiral pairing state as a higher-order topological superconductor, which depending on the existence of a four-fold rotoinversion symmetry, is either intrinsic, {meaning that the corresponding hinge states can only be removed by closing the bulk gap, rather than modifying the surface states}, or extrinsic. We achieve this understanding via various methods recently developed for higher-order topology, including Wannier representability, Wannier spectrum, and defect classification approaches. For the four-fold rotoinversion symmetric case, we provide a complete classification of the higher-order topological superconductors. We show that such second-order topological superconductors exhibit chiral hinge modes that are robust in the absence of interaction effects but can be eliminated at the cost of introducing surface topological order.

  11 citations

• Exotic invertible phases with higher-group symmetries

  Po-Shen Hsin, Wenjie Ji, Chao-Ming Jian

  SciPost Phys. 12, 052 (2022) · published 3 February 2022 | Toggle abstract · pdf

  We investigate a family of invertible phases of matter with higher-dimensional exotic excitations in even spacetime dimensions, which includes and generalizes the Kitaev's chain in 1+1d. The excitation has $\mathbb{Z}_2$ higher-form symmetry that mixes with the spacetime Lorentz symmetry to form a higher group spacetime symmetry. We focus on the invertible exotic loop topological phase in 3+1d. This invertible phase is protected by the $\mathbb{Z}_2$ one-form symmetry and the time-reversal symmetry, and has surface thermal Hall conductance not realized in conventional time-reversal symmetric ordinary bosonic systems without local fermion particles and the exotic loops. We describe a UV realization of the invertible exotic loop topological order using the $SO(3)_-$ gauge theory with unit discrete theta parameter, which enjoys the same spacetime two-group symmetry. We discuss several applications including the analogue of ``fermionization'' for ordinary bosonic theories with $\mathbb{Z}_2$ non-anomalous internal higher-form symmetry and time-reversal symmetry.

  13 citations

• Volume-preserving diffeomorphism as nonabelian higher-rank gauge symmetry

  Yi-Hsien Du, Umang Mehta, Dung Xuan Nguyen, Dam Thanh Son

  SciPost Phys. 12, 050 (2022) · published 2 February 2022 | Toggle abstract · pdf

  We propose nonabelian higher-rank gauge theories in 2+1D and 3+1D. The gauge group is constructed from the volume-preserving diffeomorphisms of space. We show that the intriguing physics of the lowest Landau level (LLL) limit can be interpreted as the consequences of the symmetry. We derive the renowned Girvin-MacDonald-Platzman (GMP) algebra as well as the topological Wen-Zee term within our formalism. Using the gauge symmetry in 2+1D, we derive the LLL effective action of vortex crystal in rotating Bose gas as well as Wigner crystal of electron in an applied magnetic field. We show that the non-linear sigma models of ferromagnet in 2+1D and 3+1D exhibit the higher-rank gauge symmetries that we introduce in this paper. We interpret the fractonic behavior of the excitations on the lowest Landau level and of skyrmions in ferromagnets as the consequence of the higher-rank gauge symmetry.

  19 citations

• Statistics of Green's functions on a disordered Cayley tree and the validity of forward scattering approximation

  Pavel A. Nosov, Ivan M. Khaymovich, Andrey Kudlis, Vladimir E. Kravtsov

  SciPost Phys. 12, 048 (2022) · published 1 February 2022 | Toggle abstract · pdf

  The accuracy of the forward scattering approximation for two-point Green's functions of the Anderson localization model on the Cayley tree is studied. A relationship between the moments of the Green's function and the largest eigenvalue of the linearized transfer-matrix equation is proved in the framework of the supersymmetric functional-integral method. The new large-disorder approximation for this eigenvalue is derived and its accuracy is established. Using this approximation the probability distribution of the two-point Green's function is found and compared with that in the forward scattering approximation (FSA). It is shown that FSA overestimates the role of resonances and thus the probability for the Green's function to be significantly larger than its typical value. The error of FSA increases with increasing the distance between points in a two-point Green's function.

  5 citations

• Constraints on beta functions in field theories

  Han Ma, Sung-Sik Lee

  SciPost Phys. 12, 046 (2022) · published 1 February 2022 | Toggle abstract · pdf

  The $\beta$-functions describe how couplings run under the renormalization group flow in field theories. In general, all couplings that respect the symmetry and locality are generated under the renormalization group flow, and the exact renormalization group flow is characterized by the $\beta$-functions defined in the infinite dimensional space of couplings. In this paper, we show that the renormalization group flow is highly constrained so that the $\beta$-functions defined in a measure zero subspace of couplings completely determine the $\beta$-functions in the entire space of couplings. We provide a quantum renormalization group-based algorithm for reconstructing the full $\beta$-functions from the $\beta$-functions defined in the subspace. As examples, we derive the full $\beta$-functions for the $O(N)$ vector model and the $O_L(N) \times O_R(N)$ matrix model entirely from the $\beta$-functions defined in the subspace of single-trace couplings.

  2 citations

• On the dynamics of free-fermionic tau-functions at finite temperature

  Daniel Chernowitz, Oleksandr Gamayun

  SciPost Phys. Core 5, 006 (2022) · published 31 January 2022 | Toggle abstract · pdf

  In this work we explore an instance of the $\tau$-function of vertex type operators, specified in terms of a constant phase shift in a free-fermionic basis. From the physical point of view this $\tau$-function has multiple interpretations: as a correlator of Jordan-Wigner strings, a Loschmidt Echo in the Aharonov-Bohm effect, or the generating function of the local densities in the Tonks-Girardeau gas. We present the $\tau$-function as a form-factors series and tackle it from four vantage points: (i) we perform an exact summation and express it in terms of a Fredholm determinant in the thermodynamic limit, (ii) we use bosonization techniques to perform partial summations of soft modes around the Fermi surface to acquire the scaling at zero temperature, (iii) we derive large space and time asymptotic behavior for the thermal Fredholm determinant by relating it to effective form-factors with an asymptotically similar kernel, and (iv) we identify and sum the important basis elements directly through a tailor-made numerical algorithm for finite-entropy states in a free-fermionic Hilbert space. All methods confirm each other. We find that, in addition to the exponential decay in the finite-temperature case the dynamic correlation functions exhibit an extra power law in time, universal over any distribution and time scale.

  8 citations

• The one-dimensional Bose gas with strong two-body losses: the effect of the harmonic confinement

  Lorenzo Rosso, Alberto Biella, Leonardo Mazza

  SciPost Phys. 12, 044 (2022) · published 28 January 2022 | Toggle abstract · pdf

  We study the dynamics of a one-dimensional Bose gas in presence of strong two-body losses. In this dissipative quantum Zeno regime, the gas fermionises and its dynamics can be described with a simple set of rate equations. Employing the local density approximation and a Boltzmann-like dynamical equation, the description is easily extended to take into account an external potential. We show that in the absence of confinement the population is depleted in an anomalous way and that the gas behaves as a low-temperature classical gas. The harmonic confinement accelerates the depopulation of the gas and introduces a novel decay regime, which we thoroughly characterise.

  16 citations

• Surface-acoustic-wave-induced unconventional superconducting pairing

  Viktoriia Kornich

  SciPost Phys. Core 5, 005 (2022) · published 27 January 2022 | Toggle abstract · pdf

  Unconventional superconductivity is usually associated with symmetry breaking in the system. Here we consider a simple setup consisting of a solid state material with conduction electrons and an applied surface acoustic wave (SAW), that can break time and spatial translation symmetries. We study the symmetries of the possible SAW-induced order parameters, showing that even-frequency spin-triplet odd-parity order parameter can occur. We suggest different methods of how to engineer the symmetries of the order parameters using SAWs and the applications of such setups.

  1 citation

• Dissipative dynamics in the free massive boson limit of the sine-Gordon model

  Á. Bácsi, C. P. Moca, G. Zaránd, B. Dóra

  SciPost Phys. Core 5, 004 (2022) · published 27 January 2022 | Toggle abstract · pdf

  We study the dissipative dynamics of one-dimensional fermions, described in terms of the sine-Gordon model in its free massive boson or semi-classical limit, while keeping track of forward scattering processes. The system is prepared in the gapped ground state, and then coupled to environment through local currents within the Lindblad formalism. The heating dynamics of the system is followed using bosonization. The single particle density matrix exhibits correlations between the left and right moving particles. While the density matrix of right movers and left movers is translationally invariant, the left-right sector is not, corresponding to a translational symmetry breaking charge density wave state. Asymptotically, the single particle density matrix decays exponentially with exponent proportional to $-\gamma t|x|\Delta^2$ where $\gamma$ and $\Delta$ are the dissipative coupling and the gap, respectively. The charge density wave order parameter decays exponentially in time with an interaction independent decay rate. The second R\'enyi entropy grows linearly with time and is essentially insensitive to the presence of the gap.

  4 citations

• Berezinskii-Kosterlitz-Thouless transition transport in spin-triplet superconductor

  Suk Bum Chung, Se Kwon Kim

  SciPost Phys. Core 5, 003 (2022) · published 27 January 2022 | Toggle abstract · pdf

  As the spin-triplet superconductivity arises from the condensation of spinful Cooper pairs, its full characterization requires not only charge ordering, but also spin ordering. For a two-dimensional (2D) easy-plane spin-triplet superconductor, this naively seems to suggest the possibility of two distinct Berezinskii-Kosterlitz-Thouless (BKT) phase transitions, one in the charge sector and the other in the spin sector. However, it has been recognized that there are actually three possible BKT transitions, involving the deconfinement of, respectively, the conventional vortices, the merons and the half-quantum vortices with vorticity in both the charge and the spin current. By considering equal-spin-pairing spin-triplet superconductors with bulk spin degeneracy, we show how all the transitions can be characterized by the relation between the voltage drop and the spin-polarized current bias. This study reveals that, due to the hitherto unexamined transport of half-quantum vortices, there is an upper bound on the spin supercurrent in a quasi-long range ordered spin-triplet superconductor, which provides a means for half-quantum vortex detection via transport measurements and deeper understanding of fluctuation effects in superconductor-based spintronic devices.

  5 citations