Publications

Order by: publication date number of citations

• Computing the eigenstate localisation length at very low energies from Localisation Landscape Theory

  Sophie S. Shamailov, Dylan J. Brown, Thomas A. Haase, Maarten D. Hoogerland

  SciPost Phys. Core 4, 017 (2021) · published 9 June 2021 | Toggle abstract · pdf

  While Anderson localisation is largely well-understood, its description has traditionally been rather cumbersome. A recently-developed theory -- Localisation Landscape Theory (LLT) -- has unparalleled strengths and advantages, both computational and conceptual, over alternative methods. To begin with, we demonstrate that the localisation length cannot be conveniently computed starting directly from the exact eigenstates, thus motivating the need for the LLT approach. Then, we confirm that the Hamiltonian with the effective potential of LLT has very similar low energy eigenstates to that with the physical potential, justifying the crucial role the effective potential plays in our new method. We proceed to use LLT to calculate the localisation length for very low-energy, maximally localised eigenstates, as defined by the length-scale of exponential decay of the eigenstates, (manually) testing our findings against exact diagonalisation. We then describe several mechanisms by which the eigenstates spread out at higher energies where the tunnelling-in-the-effective-potential picture breaks down, and explicitly demonstrate that our method is no longer applicable in this regime. We place our computational scheme in context by explaining the connection to the more general problem of multidimensional tunnelling and discussing the approximations involved. Our method of calculating the localisation length can be applied to (nearly) arbitrary disordered, continuous potentials at very low energies.

  4 citations

• Topological states between inversion symmetric atomic insulators

  Ana Silva, Jasper van Wezel

  SciPost Phys. 10, 137 (2021) · published 8 June 2021 | Toggle abstract · pdf

  One of the hallmarks of topological insulators is the correspondence between the value of its bulk topological invariant and the number of topologically protected edge modes observed in a finite-sized sample. This bulk-boundary correspondence has been well-tested for strong topological invariants, and forms the basis for all proposed technological applications of topology. Here, we report that a group of weak topological invariants, which depend only on the symmetries of the atomic lattice, also induces a particular type of bulk-boundary correspondence. It predicts the presence or absence of states localised at the interface between two inversion-symmetric band insulators with trivial values for their strong invariants, based on the space group representation of the bands on either side of the junction. We show that this corresponds with symmetry-based classifications of topological materials. The interface modes are protected by the combination of band topology and symmetry of the interface, and may be used for topological transport and signal manipulation in heterojunction-based devices.

  1 citation

• Putting a spin on metamaterials: Mechanical incompatibility as magnetic frustration

  Ben Pisanty, Erdal C. Oguz, Cristiano Nisoli, Yair Shokef

  SciPost Phys. 10, 136 (2021) · published 8 June 2021 | Toggle abstract · pdf

  Mechanical metamaterials present a promising platform for seemingly impossible mechanics. They often require incompatibility of their elementary building blocks, yet a comprehensive understanding of its role remains elusive. Relying on an analogy to ferromagnetic and antiferromagnetic binary spin interactions, we present a universal approach to identify and analyze topological mechanical defects for arbitrary building blocks. We underline differences between two- and three-dimensional metamaterials, and show how topological defects can steer stresses and strains in a controlled and non-trivial manner and can inspire the design of materials with hitherto unknown complex mechanical response.

  7 citations

• Duality in quantum transport models

  Rouven Frassek, Cristian Giardinà, Jorge Kurchan

  SciPost Phys. 10, 135 (2021) · published 8 June 2021 | Toggle abstract · pdf

  We develop the 'duality approach', that has been extensively studied for classical models of transport, for quantum systems in contact with a thermal 'Lindbladian' bath. The method provides (a) a mapping of the original model to a simpler one, containing only a few particles and (b) shows that any dynamic process of this kind with generic baths may be mapped onto one with equilibrium baths. We exemplify this through the study of a particular model: the quantum symmetric exclusion process introduced in [D. Bernard, T. Jin, Phys. Rev. Lett. 123, 080601 (2019)]. As in the classical case, the whole construction becomes intelligible by considering the dynamical symmetries of the problem.

  4 citations

• Analyticity of critical exponents of the $O(N)$ models from nonperturbative renormalization

  Andrzej Chlebicki, Pawel Jakubczyk

  SciPost Phys. 10, 134 (2021) · published 7 June 2021 | Toggle abstract · pdf

  We employ the functional renormalization group framework at the second order in the derivative expansion to study the $O(N)$ models continuously varying the number of field components $N$ and the spatial dimensionality $d$. We in particular address the Cardy-Hamber prediction concerning nonanalytical behavior of the critical exponents $\nu$ and $\eta$ across a line in the $(d,N)$ plane, which passes through the point $(2,2)$. By direct numerical evaluation of $\eta(d,N)$ and $\nu^{-1}(d,N)$ as well as analysis of the functional fixed-point profiles, we find clear indications of this line in the form of a crossover between two regimes in the $(d,N)$ plane, however no evidence of discontinuous or singular first and second derivatives of these functions for $d>2$. The computed derivatives of $\eta(d,N)$ and $\nu^{-1}(d,N)$ become increasingly large for $d\to 2$ and $N\to 2$ and it is only in this limit that $\eta(d,N)$ and $\nu^{-1}(d,N)$ as obtained by us are evidently nonanalytical. By scanning the dependence of the subleading eigenvalue of the RG transformation on $N$ for $d>2$ we find no indication of its vanishing as anticipated by the Cardy-Hamber scenario. For dimensionality $d$ approaching 3 there are no signatures of the Cardy-Hamber line even as a crossover and its existence in the form of a nonanalyticity of the anticipated form is excluded.

  10 citations

• CP symmetry and symplectic modular invariance

  Gui-Jun Ding, Ferruccio Feruglio, Xiang-Gan Liu

  SciPost Phys. 10, 133 (2021) · published 7 June 2021 | Toggle abstract · pdf

  We analyze CP symmetry in symplectic modular-invariant supersymmetric theories. We show that for genus $g\ge 3$ the definition of CP is unique, while two independent possibilities are allowed when $g\le 2$. We discuss the transformation properties of moduli, matter multiplets and modular forms in the Siegel upper half plane, as well as in invariant subspaces. We identify CP-conserving surfaces in the fundamental domain of moduli space. We make use of all these elements to build a CP and symplectic invariant model of lepton masses and mixing angles, where known data are well reproduced and observable phases are predicted in terms of a minimum number of parameters.

  35 citations

• Thermodynamic Casimir forces in strongly anisotropic systems within the $N\to \infty$ class

  Maciej Łebek, Paweł Jakubczyk

  SciPost Phys. Core 4, 016 (2021) · published 7 June 2021 | Toggle abstract · pdf

  We analyze the thermodynamic Casimir effect in strongly anizotropic systems from the vectorial $N\to\infty$ class in a slab geometry. Employing the imperfect (mean-field) Bose gas as a representative example, we demonstrate the key role of spatial dimensionality $d$ in determining the character of the effective fluctuation-mediated interaction between the confining walls. For a particular, physically conceivable choice of anisotropic dispersion and periodic boundary conditions, we show that the Casimir force at criticality as well as within the low-temperature phase is repulsive for dimensionality $d\in (\frac{5}{2},4)\cup (6,8)\cup (10,12)\cup\dots$ and attractive for $d\in (4,6)\cup (8,10)\cup \dots$. We argue, that for $d\in\{4,6,8\dots\}$ the Casimir interaction entirely vanishes in the scaling limit. We discuss implications of our results for systems characterized by $1/N>0$ and possible realizations in the context of quantum phase transitions.

  4 citations

• Branch point twist field form factors in the sine-Gordon model I: Breather fusion and entanglement dynamics

  Olalla A. Castro-Alvaredo, David X. Horvath

  SciPost Phys. 10, 132 (2021) · published 4 June 2021 | Toggle abstract · pdf

  The quantum sine-Gordon model is the simplest massive interacting integrable quantum field theory whose two-particle scattering matrix is generally non-diagonal. As such, it is a model that has been extensively studied, especially in the context of the bootstrap programme. In this paper we compute the form factors of a special local field known as the branch point twist field, whose correlation functions are building blocks for measures of entanglement. We consider the attractive regime where the theory posesses a particle spectrum consisting of a soliton, an antisoliton (of opposite $U(1)$ charges) and several (neutral) breathers. In the breather sector we exploit the fusion procedure to compute form factors of heavier breathers from those of lighter ones. We apply our results to the study of the entanglement dynamics after a small mass quench and for short times. We show that in the presence of two or more breathers the von Neumann and R\'enyi entropies display undamped oscillations in time, whose frequencies are proportional to the even breather masses and whose amplitudes are proportional to the breather's one-particle form factor.

  12 citations

• Kaluza-Klein spectrometry for ${\rm AdS_{3}}$ vacua

  Camille Eloy

  SciPost Phys. 10, 131 (2021) · published 4 June 2021 | Toggle abstract · pdf

  We use exceptional field theory to compute Kaluza-Klein mass spectra around ${\rm AdS_{3}}$ vacua that sit in half-maximal gauged supergravity in three dimensions. The formalism applies to any vacuum that arises from a consistent truncation of higher-dimensional supergravity, no matter what symmetries are preserved. We illustrate its efficiency by computing the spectra of ${\cal N}=(2,0)$ and ${\cal N}=(1,1)$ six-dimensional supergravities on ${\rm AdS_{3}}\times S^{3}$ and of type II supergravity on ${\rm AdS_{3}}\times S^{3}\times S^{3}\times S^{1}$.

  14 citations

• The quasilocal degrees of freedom of Yang-Mills theory

  Henrique Gomes, Aldo Riello

  SciPost Phys. 10, 130 (2021) · published 4 June 2021 | Toggle abstract · pdf

  Gauge theories possess nonlocal features that, in the presence of boundaries, inevitably lead to subtleties. We employ geometric methods rooted in the functional geometry of the phase space of Yang-Mills theories to: (\textit{1}) characterize a basis for quasilocal degrees of freedom (dof) that is manifestly gauge-covariant also at the boundary; (\textit{2}) tame the non-additivity of the regional symplectic forms upon the gluing of regions; and to (\textit{3}) discuss gauge and global charges in both Abelian and non-Abelian theories from a geometric perspective. Naturally, our analysis leads to splitting the Yang-Mills dof into Coulombic and radiative. Coulombic dof enter the Gauss constraint and are dependent on extra boundary data (the electric flux); radiative dof are unconstrained and independent. The inevitable non-locality of this split is identified as the source of the symplectic non-additivity, i.e. of the appearance of new dof upon the gluing of regions. Remarkably, these new dof are fully determined by the regional radiative dof only. Finally, a direct link is drawn between this split and Dirac's dressed electron.

  10 citations