Publications

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• A degeneracy bound for homogeneous topological order

  Jeongwan Haah

  SciPost Phys. 10, 011 (2021) · published 20 January 2021 | Toggle abstract · pdf

  We introduce a notion of homogeneous topological order, which is obeyed by most, if not all, known examples of topological order including fracton phases on quantum spins (qudits). The notion is a condition on the ground state subspace, rather than on the Hamiltonian, and demands that given a collection of ball-like regions, any linear transformation on the ground space be realized by an operator that avoids the ball-like regions. We derive a bound on the ground state degeneracy $\mathcal D$ for systems with homogeneous topological order on an arbitrary closed Riemannian manifold of dimension $d$, which reads \[ \log \mathcal D \le c \mu (L/a)^{d-2}.\] Here, $L$ is the diameter of the system, $a$ is the lattice spacing, and $c$ is a constant that only depends on the isometry class of the manifold, and $\mu$ is a constant that only depends on the density of degrees of freedom. If $d=2$, the constant $c$ is the (demi)genus of the space manifold. This bound is saturated up to constants by known examples.

  10 citations

• Boundary RG flows for fermions and the mod 2 anomaly

  Philip Boyle Smith, David Tong

  SciPost Phys. 10, 010 (2021) · published 19 January 2021 | Toggle abstract · pdf

  Boundary conditions for Majorana fermions in d=1+1 dimensions fall into one of two SPT phases, associated to a mod 2 anomaly. Here we consider boundary conditions for 2N Majorana fermions that preserve a $U(1)^N$ symmetry. In general, the left-moving and right-moving fermions carry different charges under this symmetry, and implementation of the boundary condition requires new degrees of freedom, which manifest themselves in a boundary central charge, $g$. We follow the boundary RG flow induced by turning on relevant boundary operators. We identify the infra-red boundary state. In many cases, the boundary state flips SPT class, resulting in an emergent Majorana mode needed to cancel the anomaly. We show that the ratio of UV and IR boundary central charges is given by $g^2_{IR} / g^2_{UV} = {\rm dim}\,({\cal O})$, the dimension of the perturbing boundary operator. Any relevant operator necessarily has ${\rm dim}({\cal O}) < 1$, ensuring that the central charge decreases in accord with the g-theorem.

  11 citations

• Diving into a holographic superconductor

  Sean A. Hartnoll, Gary T. Horowitz, Jorrit Kruthoff, Jorge E. Santos

  SciPost Phys. 10, 009 (2021) · published 15 January 2021 | Toggle abstract · pdf

  Charged black holes in anti-de Sitter space become unstable to forming charged scalar hair at low temperatures $T < T_\text{c}$. This phenomenon is a holographic realization of superconductivity. We look inside the horizon of these holographic superconductors and find intricate dynamical behavior. The spacetime ends at a spacelike Kasner singularity, and there is no Cauchy horizon. Before reaching the singularity, there are several intermediate regimes which we study both analytically and numerically. These include strong Josephson oscillations in the condensate and possible 'Kasner inversions' in which after many e-folds of expansion, the Einstein-Rosen bridge contracts towards the singularity. Due to the Josephson oscillations, the number of Kasner inversions depends very sensitively on $T$, and diverges at a discrete set of temperatures $\{T_n\}$ that accumulate at $T_c$. Near these $T_n$, the final Kasner exponent exhibits fractal-like behavior.

  41 citations

• The seniority quantum number in Tensor Network States

  Klaas Gunst, Dimitri Van Neck, Peter Andreas Limacher, Stijn De Baerdemacker

  SciPost Chem. 1, 001 (2021) · published 15 January 2021 | Toggle abstract · pdf

  We employ tensor network methods for the study of the seniority quantum number -- defined as the number of unpaired electrons in a many-body wave function -- in molecular systems. Seniority-zero methods recently emerged as promising candidates to treat strong static correlations in molecular systems, but are prone to deficiencies related to dynamical correlation and dispersion. We systematically resolve these deficiencies by increasing the allowed seniority number using tensor network methods. In particular, we investigate the number of unpaired electrons needed to correctly describe the binding of the neon and nitrogen dimer and the $D_{6h}$ symmetry of benzene.

  6 citations

• Non-equilibrium evolution of Bose-Einstein condensate deformation in temporally controlled weak disorder

  Milan Radonjić, Axel Pelster

  SciPost Phys. 10, 008 (2021) · published 14 January 2021 | Toggle abstract · pdf

  We consider a time-dependent extension of a perturbative mean-field approach to the homogeneous dirty boson problem by considering how switching on and off a weak disorder potential affects the stationary state of an initially equilibrated Bose-Einstein condensate by the emergence of a disorder-induced condensate deformation. We find that in the switch on scenario the stationary condensate deformation turns out to be a sum of an equilibrium part, that actually corresponds to adiabatic switching on the disorder, and a dynamically-induced part, where the latter depends on the particular driving protocol. If the disorder is switched off afterwards, the resulting condensate deformation acquires an additional dynamically-induced part in the long-time limit, while the equilibrium part vanishes. We also present an appropriate generalization to inhomogeneous trapped condensates. Our results demonstrate that the condensate deformation represents an indicator of the generically non-equilibrium nature of steady states of a Bose gas in a temporally controlled weak disorder.

  1 citation

• Newton series expansion of bosonic operator functions

  Jürgen König, Alfred Hucht

  SciPost Phys. 10, 007 (2021) · published 13 January 2021 | Toggle abstract · pdf

  We show how series expansions of functions of bosonic number operators are naturally derived from finite-difference calculus. The scheme employs Newton series rather than Taylor series known from differential calculus, and also works in cases where the Taylor expansion fails. For a function of number operators, such an expansion is automatically normal ordered. Applied to the Holstein-Primakoff representation of spins, the scheme yields an exact series expansion with a finite number of terms and, in addition, allows for a systematic expansion of the spin operators that respects the spin commutation relations within a truncated part of the full Hilbert space. Furthermore, the Newton series expansion strongly facilitates the calculation of expectation values with respect to coherent states. As a third example, we show that factorial moments and factorial cumulants arising in the context of photon or electron counting are a natural consequence of Newton series expansions. Finally, we elucidate the connection between normal ordering, Taylor and Newton series by determining a corresponding integral transformation, which is related to the Mellin transform.

  17 citations

• Correlation functions by separation of variables: the XXX spin chain

  Giuliano Niccoli, Hai Pei, Véronique Terras

  SciPost Phys. 10, 006 (2021) · published 12 January 2021 | Toggle abstract · pdf

  We explain how to compute correlation functions at zero temperature within the framework of the quantum version of the Separation of Variables (SoV) in the case of a simple model: the XXX Heisenberg chain of spin 1/2 with twisted (quasi-periodic) boundary conditions. We first detail all steps of our method in the case of anti-periodic boundary conditions. The model can be solved in the SoV framework by introducing inhomogeneity parameters. The action of local operators on the eigenstates are then naturally expressed in terms of multiple sums over these inhomogeneity parameters. We explain how to transform these sums over inhomogeneity parameters into multiple contour integrals. Evaluating these multiple integrals by the residues of the poles outside the integration contours, we rewrite this action as a sum involving the roots of the Baxter polynomial plus a contribution of the poles at infinity. We show that the contribution of the poles at infinity vanishes in the thermodynamic limit, and that we recover in this limit for the zero-temperature correlation functions the multiple integral representation that had been previously obtained through the study of the periodic case by Bethe Ansatz or through the study of the infinite volume model by the q-vertex operator approach. We finally show that the method can easily be generalized to the case of a more general non-diagonal twist: the corresponding weights of the different terms for the correlation functions in finite volume are then modified, but we recover in the thermodynamic limit the same multiple integral representation than in the periodic or anti-periodic case, hence proving the independence of the thermodynamic limit of the correlation functions with respect to the particular form of the boundary twist.

  6 citations

• Entanglement spreading after local fermionic excitations in the XXZ chain

  Matthias Gruber, Viktor Eisler

  SciPost Phys. 10, 005 (2021) · published 12 January 2021 | Toggle abstract · pdf

  We study the spreading of entanglement produced by the time evolution of a local fermionic excitation created above the ground state of the XXZ chain. The resulting entropy profiles are investigated via density-matrix renormalization group calculations, and compared to a quasiparticle ansatz. In particular, we assume that the entanglement is dominantly carried by spinon excitations traveling at different velocities, and the entropy profile is reproduced by a probabilistic expression involving the density fraction of the spinons reaching the subsystem. The ansatz works well in the gapless phase for moderate values of the XXZ anisotropy, eventually deteriorating as other types of quasiparticle excitations gain spectral weight. Furthermore, if the initial state is excited by a local Majorana fermion, we observe a nontrivial rescaling of the entropy profiles. This effect is further investigated in a conformal field theory framework, carrying out calculations for the Luttinger liquid theory. Finally, we also consider excitations creating an antiferromagnetic domain wall in the gapped phase of the chain, and find again a modified quasiparticle ansatz with a multiplicative factor.

  10 citations

• Sixfold fermion near the Fermi level in cubic PtBi2

  S. Thirupathaiah, Y. S. Kushnirenk, K. Koepernik, B. R. Piening, B. Buechner, S. Aswartham, J. van den Brink, S. V. Borisenko, I. C. Fulga

  SciPost Phys. 10, 004 (2021) · published 11 January 2021 | Toggle abstract · pdf

  We show that the cubic compound PtBi2, is a topological semimetal hosting a sixfold band touching point in close proximity to the Fermi level. Using angle-resolved photoemission spectroscopy, we map the bandstructure of the system, which is in good agreement with results from density functional theory. Further, by employing a low energy effective Hamiltonian valid close to the crossing point, we study the effect of a magnetic field on the sixfold fermion. The latter splits into a total of twenty Weyl cones for a Zeeman field oriented in the diagonal, [111] direction. Our results mark cubic PtBi2, as an ideal candidate to study the transport properties of gapless topological systems beyond Dirac and Weyl semimetals.

  8 citations

• Exotic $\mathbb{Z}_N$ symmetries, duality, and fractons in 3+1-dimensional quantum field theory

  Nathan Seiberg, Shu-Heng Shao

  SciPost Phys. 10, 003 (2021) · published 8 January 2021 | Toggle abstract · pdf

  Following our earlier analyses of nonstandard continuum quantum field theories, we study here gapped systems in 3+1 dimensions, which exhibit fractonic behavior. In particular, we present three dual field theory descriptions of the low-energy physics of the X-cube model. A key aspect of our constructions is the use of discontinuous fields in the continuum field theory. Spacetime is continuous, but the fields are not.

  68 citations