Publications

Order by: publication date number of citations

• The Loschmidt Index

  Diego Liska, Vladimir Gritsev

  SciPost Phys. 10, 100 (2021) · published 4 May 2021 | Toggle abstract · pdf

  We study the nodes of the wavefunction overlap between ground states of a parameter-dependent Hamiltonian. These nodes are topological, and we can use them to analyze in a unifying way both equilibrium and dynamical quantum phase transitions in multi-band systems. We define the Loschmidt index as the number of nodes in this overlap and discuss the relationship between this index and the wrapping number of a closed auxiliary hypersurface. This relationship allows us to compute this index systematically, using an integral representation of the wrapping number. We comment on the relationship between the Loschmidt index and other well-established topological numbers. As an example, we classify the equilibrium and dynamical quantum phase transitions of the XY model by counting the nodes in the wavefunction overlaps.

  6 citations

• The folded spin-1/2 XXZ model: II. Thermodynamics and hydrodynamics with a minimal set of charges

  Lenart Zadnik, Kemal Bidzhiev, Maurizio Fagotti

  SciPost Phys. 10, 099 (2021) · published 3 May 2021 | Toggle abstract · pdf

  We study the (dual) folded spin-1/2 XXZ model in the thermodynamic limit. We focus, in particular, on a class of local macrostates that includes Gibbs ensembles. We develop a thermodynamic Bethe Ansatz description and work out generalised hydrodynamics at the leading order. Remarkably, in the ballistic scaling limit the junction of two local macrostates results in a discontinuity in the profile of essentially any local observable.

  52 citations

• STrEAMlining EFT Matching

  Timothy Cohen, Xiaochuan Lu, Zhengkang Zhang

  SciPost Phys. 10, 098 (2021) · published 3 May 2021 | Toggle abstract · pdf

  This paper presents STrEAM (SuperTrace Evaluation Automated for Matching), a Mathematica package that calculates all functional supertraces which arise when matching a generic UV model onto a relativistic Effective Field Theory (EFT) at one loop and to arbitrary order in the heavy mass expansion. STrEAM implements the covariant derivative expansion to automate the most tedious step of the streamlined functional matching prescription presented in arXiv:2011.02484 . The code and an example notebook are available at https://www.github.com/EFTMatching/STrEAM .

  47 citations

• 3d N=4 Bootstrap and Mirror Symmetry

  Chi-Ming Chang, Martin Fluder, Ying-Hsuan Lin, Shu-Heng Shao, Yifan Wang

  SciPost Phys. 10, 097 (2021) · published 30 April 2021 | Toggle abstract · pdf

  We investigate the non-BPS realm of 3d ${\cal N} = 4$ superconformal field theory by uniting the non-perturbative methods of the conformal bootstrap and supersymmetric localization, and utilizing special features of 3d ${\cal N} = 4$ theories such as mirror symmetry and a protected sector described by topological quantum mechanics (TQM). Supersymmetric localization allows for the exact determination of the conformal and flavor central charges, and the latter can be fed into the mini-bootstrap of the TQM to solve for a subset of the OPE data. We examine the implications of the $\mathbb{Z}_2$ mirror action for the SCFT single- and mixed-branch crossing equations for the moment map operators, and apply numerical bootstrap to obtain universal constraints on OPE data for given flavor symmetry groups. A key ingredient in applying the bootstrap analysis is the determination of the mixed-branch superconformal blocks. Among other results, we show that the simplest known self-mirror theory with $SU(2) \times SU(2)$ flavor symmetry saturates our bootstrap bounds, which allows us to extract the non-BPS data and examine the self-mirror $\mathbb{Z}_2$ symmetry thereof.

  12 citations

• A general definition of $JT_a$ -- deformed QFTs

  Tarek Anous, Monica Guica

  SciPost Phys. 10, 096 (2021) · published 30 April 2021 | Toggle abstract · pdf

  We propose a general path-integral definition of two-dimensional quantum field theories deformed by an integrable, irrelevant vector operator constructed from the components of the stress tensor and those of a $U(1)$ current. The deformed theory is obtained by coupling the original QFT to a flat dynamical gauge field and "half" a flat dynamical vielbein. The resulting partition function is shown to satisfy a geometric flow equation, which perfectly reproduces the flow equations for the deformed energy levels that were previously derived in the literature. The S-matrix of the deformed QFT differs from the original S-matrix only by an overall phase factor that depends on the charges and momenta of the external particles, thus supporting the conjecture that such QFTs are UV complete, although intrinsically non-local. For the special case of an integrable QFT, we check that this phase factor precisely reproduces the change in the finite-size spectrum via the Thermodynamic Bethe Ansatz equations.

  11 citations

• Generalized hydrodynamics in complete box-ball system for $U_q(\widehat{sl}_n)$

  Atsuo Kuniba, Grégoire Misguich, Vincent Pasquier

  SciPost Phys. 10, 095 (2021) · published 30 April 2021 | Toggle abstract · pdf

  We introduce the complete box-ball system (cBBS), which is an integrable cellular automaton on 1D lattice associated with the quantum group $U_q(\widehat{sl}_n)$. Compared with the conventional $(n-1)$-color BBS, it enjoys a remarkable simplification that scattering of solitons is totally diagonal. We also submit the cBBS to randomized initial conditions and study its non-equilibrium behavior by thermodynamic Bethe ansatz and generalized hydrodynamics. Excellent agreement is demonstrated between theoretical predictions and numerical simulation on the density plateaux generated from domain wall initial conditions including their diffusive broadening.

  3 citations

• Screw dislocations in the X-cube fracton model

  Nandagopal Manoj, Kevin Slagle, Wilbur Shirley, Xie Chen

  SciPost Phys. 10, 094 (2021) · published 29 April 2021 | Toggle abstract · pdf

  The X-cube model, a prototypical gapped fracton model, has been shown to have a foliation structure. That is, inside the 3+1D model, there are hidden layers of 2+1D gapped topological states. A screw dislocation in a 3+1D lattice can often reveal nontrivial features associated with a layered structure. In this paper, we study the X-cube model on lattices with screw dislocations. In particular, we find that a screw dislocation results in a finite change in the logarithm of the ground state degeneracy of the model. Part of the change can be traced back to the effect of screw dislocations in a simple stack of 2+1D topological states, hence corroborating the foliation structure in the model. The other part of the change comes from the induced motion of fractons or sub-dimensional excitations along the dislocation, a feature absent in the stack of 2+1D layers.

  9 citations

• Charge quantization and detector resolution

  Roman-Pascal Riwar

  SciPost Phys. 10, 093 (2021) · published 29 April 2021 | Toggle abstract · pdf

  Charge quantization, or the absence thereof, is a central theme in quantum circuit theory, with dramatic consequences for the predicted circuit dynamics. Very recently, the question of whether or not charge should actually be described as quantized has enjoyed renewed widespread interest, with however seemingly contradictory propositions. Here, we intend to reconcile these different approaches, by arguing that ultimately, charge quantization is not an intrinsic system property, but instead depends on the spatial resolution of the charge detector. We show that the latter can be directly probed by unique geometric signatures in the correlations of the supercurrent. We illustrate these findings at the example of Josephson junction arrays in the superinductor regime, where the transported charge appears to be continuous. Finally, we comment on potential consequences of charge quantization beyond superconducting circuits.

  5 citations

• Bulk-boundary-defect correspondence at disclinations in rotation-symmetric topological insulators and superconductors

  Max Geier, Ion Cosma Fulga, Alexander Lau

  SciPost Phys. 10, 092 (2021) · published 26 April 2021 | Toggle abstract · pdf

  We study a link between the ground-state topology and the topology of the lattice via the presence of anomalous states at disclinations -- topological lattice defects that violate a rotation symmetry only locally. We first show the existence of anomalous disclination states, such as Majorana zero-modes or helical electronic states, in second-order topological phases by means of Volterra processes. Using the framework of topological crystals to construct $d$-dimensional crystalline topological phases with rotation and translation symmetry, we then identify all contributions to $(d-2)$-dimensional anomalous disclination states from weak and first-order topological phases. We perform this procedure for all Cartan symmetry classes of topological insulators and superconductors in two and three dimensions and determine whether the correspondence between bulk topology, boundary signatures, and disclination anomaly is unique.

  25 citations

• Low rank compression in the numerical solution of the nonequilibrium Dyson equation

  Jason Kaye, Denis Golež

  SciPost Phys. 10, 091 (2021) · published 26 April 2021 | Toggle abstract · pdf

  We propose a method to improve the computational and memory efficiency of numerical solvers for the nonequilibrium Dyson equation in the Keldysh formalism. It is based on the empirical observation that the nonequilibrium Green's functions and self energies arising in many problems of physical interest, discretized as matrices, have low rank off-diagonal blocks, and can therefore be compressed using a hierarchical low rank data structure. We describe an efficient algorithm to build this compressed representation on the fly during the course of time stepping, and use the representation to reduce the cost of computing history integrals, which is the main computational bottleneck. For systems with the hierarchical low rank property, our method reduces the computational complexity of solving the nonequilibrium Dyson equation from cubic to near quadratic, and the memory complexity from quadratic to near linear. We demonstrate the full solver for the Falicov-Kimball model exposed to a rapid ramp and Floquet driving of system parameters, and are able to increase feasible propagation times substantially. We present examples with 262144 time steps, which would require approximately five months of computing time and 2.2 TB of memory using the direct time stepping method, but can be completed in just over a day on a laptop with less than 4 GB of memory using our method. We also confirm the hierarchical low rank property for the driven Hubbard model in the weak coupling regime within the GW approximation, and in the strong coupling regime within dynamical mean-field theory.

  38 citations