Publications

Order by: publication date number of citations

• Abelian and non-abelian symmetries in infinite projected entangled pair states

  Claudius Hubig

  SciPost Phys. 5, 047 (2018) · published 9 November 2018 | Toggle abstract · pdf

  We explore in detail the implementation of arbitrary abelian and non-abelian symmetries in the setting of infinite projected entangled pair states on the two-dimensional square lattice. We observe a large computational speed-up; easily allowing bond dimensions $D = 10$ in the square lattice Heisenberg model at computational effort comparable to calculations at $D = 6$ without symmetries. We also find that implementing an unbroken symmetry does not negatively affect the representative power of the state and leads to identical or improved ground-state energies. Finally, we point out how to use symmetry implementations to detect spontaneous symmetry breaking.

  16 citations

• A non-Abelian parton state for the $ν=2+3/8$ fractional quantum Hall effect

  Ajit Coimbatore Balram

  SciPost Phys. 10, 083 (2021) · published 15 April 2021 | Toggle abstract · pdf

  Fascinating structures have arisen from the study of the fractional quantum Hall effect (FQHE) at the even denominator fraction of $5/2$. We consider the FQHE at another even denominator fraction, namely $\nu=2+3/8$, where a well-developed and quantized Hall plateau has been observed in experiments. We examine the non-Abelian state described by the "$\bar{3}\bar{2}^{2}1^{4}$" parton wave function and numerically demonstrate it to be a feasible candidate for the ground state at $\nu=2+3/8$. We make predictions for experimentally measurable properties of the $\bar{3}\bar{2}^{2}1^{4}$ state that can reveal its underlying topological structure.

  16 citations

• Kibble–Zurek mechanism in the Ising Field Theory

  Kristóf Hódsági, Marton Kormos

  SciPost Phys. 9, 055 (2020) · published 20 October 2020 | Toggle abstract · pdf

  The Kibble-Zurek mechanism captures universality when a system is driven through a continuous phase transition. Here we study the dynamical aspect of quantum phase transitions in the Ising Field Theory where the quantum critical point can be crossed in different directions in the two-dimensional coupling space leading to different scaling laws. Using the Truncated Conformal Space Approach, we investigate the microscopic details of the Kibble-Zurek mechanism in terms of instantaneous eigenstates in a genuinely interacting field theory. For different protocols, we demonstrate dynamical scaling in the non-adiabatic time window and provide analytic and numerical evidence for specific scaling properties of various quantities. In particular, we argue that the higher cumulants of the excess heat exhibit universal scaling in generic interacting models for a slow enough ramp.

  16 citations

• Bootstrapping mixed correlators in three-dimensional cubic theories II

  Stefanos R. Kousvos, Andreas Stergiou

  SciPost Phys. 8, 085 (2020) · published 9 June 2020 | Toggle abstract · pdf

  Conformal field theories (CFTs) with cubic global symmetry in 3D are relevant in a variety of condensed matter systems and have been studied extensively with the use of perturbative methods like the $\varepsilon$ expansion. In an earlier work, we used the nonperturbative numerical conformal bootstrap to provide evidence for the existence of a previously unknown 3D CFT with cubic symmetry, dubbed "Platonic CFT". In this work, we make further use of the numerical conformal bootstrap to perform a three-dimensional scan in the space of scaling dimensions of three low-lying operators. We find a three-dimensional isolated allowed region in parameter space, which includes both the 3D (decoupled) Ising model and the Platonic CFT. The essential assumptions on the spectrum of operators used to provide the isolated allowed region include the existence of a stress-energy tensor and the irrelevance of certain operators (in the renormalization group sense).

  16 citations

• Page curve for entanglement negativity through geometric evaporation

  Jaydeep Kumar Basak, Debarshi Basu, Vinay Malvimat, Himanshu Parihar, Gautam Sengupta

  SciPost Phys. 12, 004 (2022) · published 5 January 2022 | Toggle abstract · pdf

  We compute the entanglement negativity for various pure and mixed state configurations in a bath coupled to an evaporating two dimensional non-extremal Jackiw-Teitelboim (JT) black hole obtained through the partial dimensional reduction of a three dimensional BTZ black hole. Our results exactly reproduce the analogues of the Page curve for the entanglement negativity which were recently determined through diagrammatic technique developed in the context of random matrix theory.

  16 citations

• Zero temperature momentum distribution of an impurity in a polaron state of one-dimensional Fermi and Tonks-Girardeau gases

  Oleksandr Gamayun, Oleg Lychkovskiy, Mikhail B. Zvonarev

  SciPost Phys. 8, 053 (2020) · published 7 April 2020 | Toggle abstract · pdf

  We investigate the momentum distribution function of a single distinguishable impurity particle which formed a polaron state in a gas of either free fermions or Tonks-Girardeau bosons in one spatial dimension. We obtain a Fredholm determinant representation of the distribution function for the Bethe ansatz solvable model of an impurity-gas δ-function interaction potential at zero temperature, in both repulsive and attractive regimes. We deduce from this representation the fourth power decay at a large momentum, and a weakly divergent (quasi-condensate) peak at a finite momentum. We also demonstrate that the momentum distribution function in the limiting case of infinitely strong interaction can be expressed through a correlation function of the one-dimensional impenetrable anyons.

  16 citations

• Fermionic Gaussian states: an introduction to numerical approaches

  Jacopo Surace, Luca Tagliacozzo

  SciPost Phys. Lect. Notes 54 (2022) · published 16 May 2022 | Toggle abstract · pdf

  This document is meant to be a practical introduction to the analytical and numerical manipulation of Fermionic Gaussian systems. Starting from the basics, we move to relevant modern results and techniques, presenting numerical examples and studying relevant Hamiltonians, such as the transverse field Ising Hamiltonian, in detail. We finish introducing novel algorithms connecting Fermionic Guassian states with matrix product states techniques. All the numerical examples make use of the free Julia package F_utilities.

  16 citations

• Holographic thermal correlators from supersymmetric instantons

  Matthew Dodelson, Alba Grassi, Cristoforo Iossa, Daniel Panea Lichtig, Alexander Zhiboedov

  SciPost Phys. 14, 116 (2023) · published 16 May 2023 | Toggle abstract · pdf

  We present an exact formula for the thermal scalar two-point function in four-dimensional holographic conformal field theories. The problem of finding it reduces to the analysis of the wave equation on the AdS-Schwarzschild background. The two-point function is computed from the connection coefficients of the Heun equation, which can be expressed in terms of the Nekrasov-Shatashvili partition function of an $SU(2)$ supersymmetric gauge theory with four fundamental hypermultiplets. The result is amenable to numerical evaluation upon truncating the number of instantons in the convergent expansion of the partition function. We also examine it analytically in various limits. At large spin the instanton expansion of the thermal two-point function directly maps to the light-cone bootstrap analysis of the heavy-light four-point function. Using this connection, we compute the OPE data of heavy-light double-twist operators. We compare our prediction to the perturbative results available in the literature and find perfect agreement.

  16 citations

• Froissart bound for/from CFT Mellin amplitudes

  Parthiv Haldar, Aninda Sinha

  SciPost Phys. 8, 095 (2020) · published 30 June 2020 | Toggle abstract · pdf

  We derive bounds analogous to the Froissart bound for the absorptive part of CFT$_d$ Mellin amplitudes. Invoking the AdS/CFT correspondence, these amplitudes correspond to scattering in AdS$_{d+1}$. We can take a flat space limit of the corresponding bound. We find the standard Froissart-Martin bound, including the coefficient in front for $d+1=4$ being $\pi/\mu^2$, $\mu$ being the mass of the lightest exchange. For $d>4$, the form is different. We show that while for $CFT_{d\leq 6}$, the number of subtractions needed to write a dispersion relation for the Mellin amplitude is equal to 2, for $CFT_{d>6}$ the number of subtractions needed is greater than 2 and goes to infinity as $d$ goes to infinity.

  16 citations

• The self-consistent quantum-electrostatic problem in strongly non-linear regime

  Pacome Armagnat, A. Lacerda-Santos, Benoit Rossignol, Christoph Groth, Xavier Waintal

  SciPost Phys. 7, 031 (2019) · published 11 September 2019 | Toggle abstract · pdf

  The self-consistent quantum-electrostatic (also known as Poisson-Schr\"odinger) problem is notoriously difficult in situations where the density of states varies rapidly with energy. At low temperatures, these fluctuations make the problem highly non-linear which renders iterative schemes deeply unstable. We present a stable algorithm that provides a solution to this problem with controlled accuracy. The technique is intrinsically convergent including in highly non-linear regimes. We illustrate our approach with (i) a calculation of the compressible and incompressible stripes in the integer quantum Hall regime and (ii) a calculation of the differential conductance of a quantum point contact geometry. Our technique provides a viable route for the predictive modeling of the transport properties of quantum nanoelectronics devices.

  16 citations