Publications

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• Entanglement gap, corners, and symmetry breaking

  Vincenzo Alba

  SciPost Phys. 10, 056 (2021) · published 8 March 2021 | Toggle abstract · pdf

  We investigate the finite-size scaling of the lowest entanglement gap $\delta\xi$ in the ordered phase of the two-dimensional quantum spherical model (QSM). The entanglement gap decays as $\delta\xi=\Omega/\sqrt{L\ln(L)}$. This is in contrast with the purely logarithmic behaviour as $\delta\xi=\pi^2/\ln(L)$ at the critical point. The faster decay in the ordered phase reflects the presence of magnetic order. We analytically determine the constant $\Omega$, which depends on the low-energy part of the model dispersion and on the geometry of the bipartition. In particular, we are able to compute the corner contribution to $\Omega$, at least for the case of a square corner.

  5 citations

• Characteristic determinant and Manakov triple for the double elliptic integrable system

  A. Grekov, A. Zotov

  SciPost Phys. 10, 055 (2021) · published 4 March 2021 | Toggle abstract · pdf

  Using the intertwining matrix of the IRF-Vertex correspondence we propose a determinant representation for the generating function of the commuting Hamiltonians of the double elliptic integrable system. More precisely, it is a ratio of the normally ordered determinants, which turns into a single determinant in the classical case. With its help we reproduce the recently suggested expression for the eigenvalues of the Hamiltonians for the dual to elliptic Ruijsenaars model. Next, we study the classical counterpart of our construction, which gives expression for the spectral curve and the corresponding $L$-matrix. This matrix is obtained explicitly as a weighted average of the Ruijsenaars and/or Sklyanin type Lax matrices with the weights as in the theta function series definition. By construction the $L$-matrix satisfies the Manakov triple representation instead of the Lax equation. Finally, we discuss the factorized structure of the $L$-matrix.

  4 citations

• Finite-size corrections in critical symmetry-resolved entanglement

  Benoit Estienne, Yacine Ikhlef, Alexi Morin-Duchesne

  SciPost Phys. 10, 054 (2021) · published 4 March 2021 | Toggle abstract · pdf

  In the presence of a conserved quantity, symmetry-resolved entanglement entropies are a refinement of the usual notion of entanglement entropy of a subsystem. For critical 1d quantum systems, it was recently shown in various contexts that these quantities generally obey entropy equipartition in the scaling limit, i.e. they become independent of the symmetry sector. In this paper, we examine the finite-size corrections to the entropy equipartition phenomenon, and show that the nature of the symmetry group plays a crucial role. In the case of a discrete symmetry group, the corrections decay algebraically with system size, with exponents related to the operators' scaling dimensions. In contrast, in the case of a U(1) symmetry group, the corrections only decay logarithmically with system size, with model-dependent prefactors. We show that the determination of these prefactors boils down to the computation of twisted overlaps.

  53 citations

• Matrix product operator symmetries and intertwiners in string-nets with domain walls

  Laurens Lootens, Jürgen Fuchs, Jutho Haegeman, Christoph Schweigert, Frank Verstraete

  SciPost Phys. 10, 053 (2021) · published 1 March 2021 | Toggle abstract · pdf

  We provide a description of virtual non-local matrix product operator (MPO) symmetries in projected entangled pair state (PEPS) representations of string-net models. Given such a PEPS representation, we show that the consistency conditions of its MPO symmetries amount to a set of six coupled equations that can be identified with the pentagon equations of a bimodule category. This allows us to classify all equivalent PEPS representations and build MPO intertwiners between them, synthesising and generalising the wide variety of tensor network representations of topological phases. Furthermore, we use this generalisation to build explicit PEPS realisations of domain walls between different topological phases as constructed by Kitaev and Kong [Commun. Math. Phys. 313 (2012) 351-373]. While the prevailing abstract categorical approach is sufficient to describe the structure of topological phases, explicit tensor network representations are required to simulate these systems on a computer, such as needed for calculating thresholds of quantum error-correcting codes based on string-nets with boundaries. Finally, we show that all these string-net PEPS representations can be understood as specific instances of Turaev-Viro state-sum models of topological field theory on three-manifolds with a physical boundary, thereby putting these tensor network constructions on a mathematically rigorous footing.

  34 citations

• Raman sideband cooling in optical tweezer arrays for Rydberg dressing

  Nikolaus Lorenz, Lorenzo Festa, Lea-Marina Steinert, Christian Gross

  SciPost Phys. 10, 052 (2021) · published 1 March 2021 | Toggle abstract · pdf

  Single neutral atoms trapped in optical tweezers and laser-coupled to Rydberg states provide a fast and flexible platform to generate configurable atomic arrays for quantum simulation. The platform is especially suited to study quantum spin systems in various geometries. However, for experiments requiring continuous trapping, inhomogeneous light shifts induced by the trapping potential and temperature broadening impose severe limitations. Here we show how Raman sideband cooling allows one to overcome those limitations, thus, preparing the stage for Rydberg dressing in tweezer arrays.

  23 citations

• Branes, quivers and wave-functions

  Taro Kimura, Miłosz Panfil, Yuji Sugimoto, Piotr Sułkowski

  SciPost Phys. 10, 051 (2021) · published 26 February 2021 | Toggle abstract · pdf

  We consider a large class of branes in toric strip geometries, both non-periodic and periodic ones. For a fixed background geometry we show that partition functions for such branes can be reinterpreted, on one hand, as quiver generating series, and on the other hand as wave-functions in various polarizations. We determine operations on quivers, as well as $SL(2,\mathbb{Z})$ transformations, which correspond to changing positions of these branes. Our results prove integrality of BPS multiplicities associated to this class of branes, reveal how they transform under changes of polarization, and imply all other properties of brane amplitudes that follow from the relation to quivers.

  7 citations

• More axions from strings

  Marco Gorghetto, Edward Hardy, Giovanni Villadoro

  SciPost Phys. 10, 050 (2021) · published 26 February 2021 | Toggle abstract · pdf

  We study the contribution to the QCD axion dark matter abundance that is produced by string defects during the so-called scaling regime. Clear evidence of scaling violations is found, the most conservative extrapolation of which strongly suggests a large number of axions from strings. In this regime, nonlinearities at around the QCD scale are shown to play an important role in determining the final abundance. The overall result is a lower bound on the QCD axion mass in the post-inflationary scenario that is substantially stronger than the naive one from misalignment.

  137 citations

• Floquet conformal field theories with generally deformed Hamiltonians

  Ruihua Fan, Yingfei Gu, Ashvin Vishwanath, Xueda Wen

  SciPost Phys. 10, 049 (2021) · published 25 February 2021 | Toggle abstract · pdf

  In this work, we study non-equilibrium dynamics in Floquet conformal field theories (CFTs) in 1+1D, in which the driving Hamiltonian involves the energy-momentum density spatially modulated by an arbitrary smooth function. This generalizes earlier work which was restricted to the sine-square deformed type of Floquet Hamiltonians, operating within a $\mathfrak{sl}_2$ sub-algebra. Here we show remarkably that the problem remains soluble in this generalized case which involves the full Virasoro algebra, based on a geometrical approach. It is found that the phase diagram is determined by the stroboscopic trajectories of operator evolution. The presence/absence of spatial fixed points in the operator evolution indicates that the driven CFT is in a heating/non-heating phase, in which the entanglement entropy grows/oscillates in time. Additionally, the heating regime is further subdivided into a multitude of phases, with different entanglement patterns and spatial distribution of energy-momentum density, which are characterized by the number of spatial fixed points. Phase transitions between these different heating phases can be achieved simply by changing the duration of application of the driving Hamiltonian. We demonstrate the general features with concrete CFT examples and compare the results to lattice calculations and find remarkable agreement.

  24 citations

• A beginner's guide to non-abelian iPEPS for correlated fermions

  Benedikt Bruognolo, Jheng-Wei Li, Jan von Delft, Andreas Weichselbaum

  SciPost Phys. Lect. Notes 25 (2021) · published 25 February 2021 | Toggle abstract · pdf

  Infinite projected entangled pair states (iPEPS) have emerged as a powerful tool for studying interacting two-dimensional fermionic systems. In this review, we discuss the iPEPS construction and some basic properties of this tensor network (TN) ansatz. Special focus is put on (i) a gentle introduction of the diagrammatic TN representations forming the basis for deriving the complex numerical algorithm, and (ii) the technical advance of fully exploiting non-abelian symmetries for fermionic iPEPS treatments of multi-band lattice models. The exploitation of non-abelian symmetries substantially increases the performance of the algorithm, enabling the treatment of fermionic systems up to a bond dimension $D=24$ on a square lattice. A variety of complex two-dimensional (2D) models thus become numerically accessible. Here, we present first promising results for two types of multi-band Hubbard models, one with $2$ bands of spinful fermions of $\mathrm{SU}(2)_\mathrm{spin} \otimes \mathrm{SU}(2)_\mathrm{orb}$ symmetry, the other with $3$ flavors of spinless fermions of $\mathrm{SU}(3)_\mathrm{flavor}$ symmetry.

  15 citations

• On the stability of the infinite Projected Entangled Pair Operator ansatz for driven-dissipative 2D lattices

  Dainius Kilda, Alberto Biella, Marco Schirò, Rosario Fazio, Jonathan Keeling

  SciPost Phys. Core 4, 005 (2021) · published 24 February 2021 | Toggle abstract · pdf

  We present calculations of the time-evolution of the driven-dissipative XYZ model using the infinite Projected Entangled Pair Operator (iPEPO) method, introduced by [A. Kshetrimayum, H. Weimer and R. Orús, Nat. Commun. 8, 1291 (2017)]. We explore the conditions under which this approach reaches a steady state. In particular, we study the conditions where apparently converged calculations may become unstable with increasing bond dimension of the tensor-network ansatz. We discuss how more reliable results could be obtained.

  11 citations