Publications

Order by: publication date number of citations

• Common framework and quadratic Bethe equations for rational Gaudin magnets in arbitrarily oriented magnetic fields

  Alexandre Faribault, Hugo Tschirhart

  SciPost Phys. 3, 009 (2017) · published 4 August 2017 | Toggle abstract · pdf

  In this work we demonstrate a simple way to implement the quantum inverse scattering method to find eigenstates of spin-1/2 XXX Gaudin magnets in an arbitrarily oriented magnetic field. The procedure differs vastly from the most natural approach which would be to simply orient the spin quantisation axis in the same direction as the magnetic field through an appropriate rotation. Instead, we define a modified realisation of the rational Gaudin algebra and use the quantum inverse scattering method which allows us, within a slightly modified implementation, to build an algebraic Bethe ansatz using the same unrotated reference state (pseudovacuum) for any external field. This common framework allows us to easily write determinant expressions for certain scalar products which would be highly non-trivial in the rotated system approach.

  11 citations

• Time-reversal-broken Weyl semimetal in the Hofstadter regime

  Faruk Abdulla, Ankur Das, Sumathi Rao, Ganpathy Murthy

  SciPost Phys. Core 5, 014 (2022) · published 16 March 2022 | Toggle abstract · pdf

  We study the phase diagram for a lattice model of a time-reversal-broken three-dimensional Weyl semimetal (WSM) in an orbital magnetic field $B$ with a flux of $p/q$ per unit cell ($0\le p \le q-1$), with minimal crystalline symmetry. We find several interesting phases: (i) WSM phases with $2q$, $4q$, $6q$, and $8q$ Weyl nodes and corresponding surface Fermi arcs, (ii) a layered Chern insulating (LCI) phase, gapped in the bulk, but with gapless surface states, (iii) a phase in which some bulk bands are gapless with Weyl nodes, coexisting with others that are gapped but topologically nontrivial, adiabatically connected to an LCI phase, (iv) a new gapped trivially insulating phase (I$'$) with (non-topological) counter-propagating surface states, which could be gapped out in the absence of crystal symmetries. Importantly, we are able to obtain the phase boundaries analytically for all $p,q$. Analyzing the gaps for $p=1$ and very large $q$ enables us to smoothly take the zero-field limit, even though the phase diagrams look ostensibly very different for $q=1, B=0$, and $q\to\infty, B\to 0$.

  11 citations

• Competing topological orders in three dimensions

  M. Mühlhauser, K. P. Schmidt , J. Vidal, M. R. Walther

  SciPost Phys. 12, 069 (2022) · published 22 February 2022 | Toggle abstract · pdf

  We study the competition between two different topological orders in three dimensions by considering the X-cube model and the three-dimensional toric code. The corresponding Hamiltonian can be decomposed into two commuting parts, one of which displaying a self-dual spectrum. To determine the phase diagram, we compute the high-order series expansions of the ground-state energy in all limiting cases. Apart from the topological order related to the toric code and the fractonic order related to the X-cube model, we found two new phases which are adiabatically connected to classical limits with nontrivial sub-extensive degeneracies. All phase transitions are found to be first order.

  11 citations

• Field Theories for type-II fractons

  Weslei B. Fontana, Pedro R. S. Gomes, Claudio Chamon

  SciPost Phys. 12, 064 (2022) · published 16 February 2022 | Toggle abstract · pdf

  We derive an effective field theory for a type-II fracton starting from the Haah code on the lattice. The effective topological theory is not given exclusively in terms of an action; it must be supplemented with a condition that selects physical states. Without the constraint, the action only describes a type-I fracton. The constraint emerges from a condition that cube operators multiply to the identity, and it cannot be consistently implemented in the continuum theory at the operator level, but only in a weaker form, in terms of matrix elements of physical states. Informed by these studies and starting from the opposite end, i.e., the continuum, we discuss a Chern-Simons-like theory that does not need a constraint or projector, and yet has no mobile excitations. Whether this continuum theory admits a lattice counterpart remains unanswered.

  11 citations

• Spin rotons and supersolids in binary antidipolar condensates

  Wyatt Kirkby, Thomas Bland, Francesca Ferlaino, Russell N. Bisset

  SciPost Phys. Core 6, 084 (2023) · published 4 December 2023 | Toggle abstract · pdf

  We present a theoretical study of a mixture of antidipolar and nondipolar Bose-Einstein condensates confined to an infinite tube. We predict the presence of a spin roton and its associated instability, which triggers a continuous unmodulated-to-supersolid phase transition. We characterize the phase diagram of the binary system, ranging from the quasi-1D to the radial Thomas-Fermi (elongated 3D) regimes. We also present the dynamic formation of supersolids following a quench from the uniform miscible phase, which maintains phase coherence across the system.

  11 citations

• Exact solution for the Lindbladian dynamics for the open XX spin chain with boundary dissipation

  Kohei Yamanaka, Tomohiro Sasamoto

  SciPost Phys. 14, 112 (2023) · published 15 May 2023 | Toggle abstract · pdf

  We obtain exact formulas for the time-dependence of a few physical observables for the open XX spin chain with Lindbladian dynamics. Our analysis is based on the fact that the Lindblad equation for an arbitrary open quadratic system of $N$ fermions is explicitly solved in terms of diagonalization of a $4N\times4N$ matrix called structure matrix by following the scheme of the third quantization. We mainly focus on the time-dependence of magnetization and spin current. As a short-time behavior at a given site, we observe the plateau regime except near the center of the chain. Basic features of this are explained by the light-cone structure created by propagations of boundary effects from the initial time, but we can explain their more detailed properties analytically using our exact formulas. On the other hand, after the plateau regime, the magnetization and spin current exhibit a slow decay to the steady state values described by the Liouvillian gap. We analytically establish its $O(N^{-3})$ scaling and also determine its coefficient.

  11 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.

  11 citations

• Anisotropic higher rank $\mathbb{Z}_N$ topological phases on graphs

  Hiromi Ebisu, Bo Han

  SciPost Phys. 14, 106 (2023) · published 11 May 2023 | Toggle abstract · pdf

  We study unusual gapped topological phases where they admit $\mathbb{Z}_N$ fractional excitations in the same manner as topologically ordered phases, yet their ground state degeneracy depends on the local geometry of the system. Placing such phases on 2D lattice, composed of an arbitrary connected graph and 1D line, we find that the fusion rules of quasiparticle excitations are described by the Laplacian of the graph and that the number of superselection sectors is related to the kernel of the Laplacian. Based on this analysis, we further show that the ground state degeneracy is given by $\bigl[N\times \prod_{i}\text{gcd}(N, p_i)\bigr]^2$, where $p_i$'s are invariant factors of the Laplacian that are greater than one and gcd stands for the greatest common divisor. We also discuss braiding statistics between quasiparticle excitations.

  11 citations

• Density-operator evolution: Complete positivity and the Keldysh real-time expansion

  Viktor Reimer, Maarten Rolf Wegewijs

  SciPost Phys. 7, 012 (2019) · published 25 July 2019 | Toggle abstract · pdf

  We study the reduced time-evolution of open quantum systems by combining quantum-information and statistical field theory. Inspired by prior work [EPL 102, 60001 (2013) and Phys. Rev. Lett. 111, 050402 (2013)] we establish the explicit structure guaranteeing the complete positivity (CP) and trace-preservation (TP) of the real-time evolution expansion in terms of the microscopic system-environment coupling. This reveals a fundamental two-stage structure of the coupling expansion: Whereas the first stage defines the dissipative timescales of the system --before having integrated out the environment completely-- the second stage sums up elementary physical processes described by CP superoperators. This allows us to establish the nontrivial relation between the (Nakajima-Zwanzig) memory-kernel superoperator for the density operator and novel memory-kernel operators that generate the Kraus operators of an operator-sum. Importantly, this operational approach can be implemented in the existing Keldysh real-time technique and allows approximations for general time-nonlocal quantum master equations to be systematically compared and developed while keeping the CP and TP structure explicit. Our considerations build on the result that a Kraus operator for a physical measurement process on the environment can be obtained by 'cutting' a group of Keldysh real-time diagrams 'in half'. This naturally leads to Kraus operators lifted to the system plus environment which have a diagrammatic expansion in terms of time-nonlocal memory-kernel operators. These lifted Kraus operators obey coupled time-evolution equations which constitute an unraveling of the original Schr\"odinger equation for system plus environment. Whereas both equations lead to the same reduced dynamics, only the former explicitly encodes the operator-sum structure of the coupling expansion.

  11 citations

• Beyond the single-site approximation modeling of electron-phonon coupling effects on resonant inelastic X-ray scattering spectra

  Krzysztof Bieniasz, Steven Johnston, Mona Berciu

  SciPost Phys. 11, 062 (2021) · published 20 September 2021 | Toggle abstract · pdf

  Resonant inelastic X-ray scattering (RIXS) is used increasingly for characterizing low-energy collective excitations in materials. RIXS is a powerful probe, which often requires sophisticated theoretical descriptions to interpret the data. In particular, the need for accurate theories describing the influence of electron-phonon ($e$-p) coupling on RIXS spectra is becoming timely, as instrument resolution improves and this energy regime is rapidly becoming accessible. To date, only rather exploratory theoretical work has been carried out for such problems. We begin to bridge this gap by proposing a versatile variational approximation for calculating RIXS spectra in weakly doped materials, for a variety of models with diverse $e$-p couplings. Here, we illustrate some of its potential by studying the role of electron mobility, which is completely neglected in the widely used local approximation based on Lang-Firsov theory. Assuming that the electron-phonon coupling is of the simplest, Holstein type, we discuss the regimes where the local approximation fails, and demonstrate that its improper use may grossly \textit{underestimate} the $e$-p coupling strength.

  11 citations