Publications

Order by: publication date number of citations

• Localization and fractality in disordered Russian Doll model

  Vedant R. Motamarri, Alexander S. Gorsky, Ivan M. Khaymovich

  SciPost Phys. 13, 117 (2022) · published 24 November 2022 | Toggle abstract · pdf

  Motivated by the interplay of Bethe-Ansatz integrability and localization in the Richardson model of superconductivity, we consider a time-reversal symmetry breaking deformation of this model, known as the Russian Doll Model (RDM), and implement diagonal on-site disorder. The localization and ergodicity-breaking properties of the single-particle spectrum are analyzed using a large-energy renormalization group (RG) over the momentum-space spectrum. Based on the above RG, we derive an effective Hamiltonian of the model, discover a fractal phase of non-ergodic delocalized states -- with the fractal dimension different from the paradigmatic Rosenzweig-Porter model -- and explain it in terms of the developed RG equations and the matrix-inversion trick.

  13 citations

• Resurgence and renormalons in the one-dimensional Hubbard model

  Marcos Mariño, Tomás Reis

  SciPost Phys. 13, 113 (2022) · published 22 November 2022 | Toggle abstract · pdf

  We use resurgent analysis to study non-perturbative aspects of the one-dimensional, multicomponent Hubbard model with an attractive interaction and arbitrary filling. In the two-component case, we show that the leading Borel singularity of the perturbative series for the ground-state energy is determined by the energy gap, as expected for superconducting systems. This singularity turns out to be of the renormalon type, and we identify a class of diagrams leading to the correct factorial growth. As a consequence of our analysis, we propose an explicit expression for the energy gap at weak coupling in the multi-component Hubbard model, at next-to-leading order in the coupling constant. In the two-component, half-filled case, we use the Bethe ansatz solution to determine the full trans-series for the ground state energy, and the exact form of its Stokes discontinuity.

  2 citations

• 2-Group symmetries and M-theory

  Michele Del Zotto, Iñaki García Etxebarria, Sakura Schäfer-Nameki

  SciPost Phys. 13, 105 (2022) · published 8 November 2022 | Toggle abstract · pdf

  Quantum Field Theories engineered in M-theory can have 2-group symmetries, mixing 0-form and 1-form symmetry backgrounds in non-trivial ways. In this paper we develop methods for determining the 2-group structure from the boundary geometry of the M-theory background. We illustrate these methods in the case of 5d theories arising from M-theory on ordinary and generalised toric Calabi-Yau cones, including cases in which the resulting theory is non-Lagrangian. Our results confirm and elucidate previous results on 2-groups from geometric engineering.

  31 citations

• Relative defects in relative theories: Trapped higher-form symmetries and irregular punctures in class S

  Lakshya Bhardwaj, Simone Giacomelli, Max Hübner, Sakura Schäfer-Nameki

  SciPost Phys. 13, 101 (2022) · published 26 October 2022 | Toggle abstract · pdf

  A relative theory is a boundary condition of a higher-dimensional topological quantum field theory (TQFT), and carries a non-trivial defect group formed by mutually non-local defects living in the relative theory. Prime examples are $6d$ $\mathcal{N}=(2,0)$ theories that are boundary conditions of $7d$ TQFTs, with the defect group arising from surface defects. In this paper, we study codimension-two defects in $6d$ $\mathcal{N}=(2,0)$ theories, and find that the line defects living inside these codimension-two defects are mutually non-local and hence also form a defect group. Thus, codimension-two defects in a $6d$ $\mathcal{N}=(2,0)$ theory are relative defects living inside a relative theory. These relative defects provide boundary conditions for topological defects of the $7d$ bulk TQFT. A codimension-two defect carrying a non-trivial defect group acts as an irregular puncture when used in the construction of $4d$ $\mathcal{N}=2$ Class S theories. The defect group associated to such an irregular puncture provides extra "trapped" contributions to the 1-form symmetries of the resulting Class S theories. We determine the defect groups associated to large classes of both conformal and non-conformal irregular punctures. Along the way, we discover many new classes of irregular punctures. A key role in the analysis of defect groups is played by two different geometric descriptions of the punctures in Type IIB string theory: one provided by isolated hypersurface singularities in Calabi-Yau threefolds, and the other provided by ALE fibrations with monodromies.

  27 citations

• Classification of Convergent OPE Channels for Lorentzian CFT Four-Point Functions

  Jiaxin Qiao

  SciPost Phys. 13, 093 (2022) · published 12 October 2022 | Toggle abstract · pdf

  We analyze the convergence properties of operator product expansions (OPE) for Lorentzian CFT four-point functions of scalar operators. We give a complete classification of Lorentzian four-point configurations. All configurations in each class have the same OPE convergence properties in s-, t- and u-channels. We give tables including the information of OPE convergence for all classes. Our work justifies that in a subset of the configuration space, Lorentzian CFT four-point functions are genuine analytic functions. Our results are valid for unitary CFTs in $d\geq2$. Our work also provides some Lorentzian regions where one can do bootstrap analysis in the sense of functions.

  1 citation

• Superspin chains from superstring theory

  Nafiz Ishtiaque, Seyed Faroogh Moosavian, Surya Raghavendran, Junya Yagi

  SciPost Phys. 13, 083 (2022) · published 5 October 2022 | Toggle abstract · pdf

  We present a correspondence between two-dimensional N=(2,2) supersymmetric gauge theories and rational integrable gl(m|n) spin chains with spin variables taking values in Verma modules. To explain this correspondence, we realize the gauge theories as configurations of branes in string theory and map them by dualities to brane configurations that realize line defects in four-dimensional Chern-Simons theory with gauge group GL(m|n). The latter configurations embed the superspin chains into superstring theory. We also provide a string theory derivation of a similar correspondence, proposed by Nekrasov, for rational gl(m|n) spin chains with spins valued in finite-dimensional representations.

  9 citations

• Generalised Onsager Algebra in Quantum Lattice Models

  Yuan Miao

  SciPost Phys. 13, 070 (2022) · published 28 September 2022 | Toggle abstract · pdf

  The Onsager algebra is one of the cornerstones of exactly solvable models in statistical mechanics. Starting from the generalised Clifford algebra, we demonstrate its relations to the graph Temperley-Lieb algebra, and a generalisation of the Onsager algebra. We present a series of quantum lattice models as representations of the generalised Clifford algebra, possessing the structure of a special type of the generalised Onsager algebra. The integrability of those models is presented, analogous to the free fermionic eight-vertex model. We also mention further extensions of the models and physical properties related to the generalised Onsager algebras, hinting at a general framework that includes families of quantum lattice models possessing the structure of the generalised Onsager algebras.

  6 citations

• Proving superintegrability in $\beta$-deformed eigenvalue models

  Aditya Bawane, Pedram Karimi, Piotr Sułkowski

  SciPost Phys. 13, 069 (2022) · published 27 September 2022 | Toggle abstract · pdf

  In this note we provide proofs of various expressions for expectation values of symmetric polynomials in $\beta$-deformed eigenvalue models with quadratic, linear, and logarithmic potentials. The relations we derive are also referred to as superintegrability. Our work completes proofs of superintegrability statements conjectured earlier in literature.

  6 citations

• Topological Orders in (4+1)-Dimensions

  Theo Johnson-Freyd, Matthew Yu

  SciPost Phys. 13, 068 (2022) · published 27 September 2022 | Toggle abstract · pdf

  We investigate the Morita equivalences of (4+1)-dimensional topological orders. We show that any (4+1)-dimensional super (fermionic) topological order admits a gapped boundary condition -- in other words, all (4+1)-dimensional super topological orders are Morita trivial. As a result, there are no inherently gapless super (3+1)-dimensional theories. On the other hand, we show that there are infinitely many algebraically Morita-inequivalent bosonic (4+1)-dimensional topological orders.

  4 citations

• Topological characterization of Lieb-Schultz-Mattis constraints and applications to symmetry-enriched quantum criticality

  Weicheng Ye, Meng Guo, Yin-Chen He, Chong Wang, Liujun Zou

  SciPost Phys. 13, 066 (2022) · published 26 September 2022 | Toggle abstract · pdf

  Lieb-Schultz-Mattis (LSM) theorems provide powerful constraints on the emergibility problem, i.e. whether a quantum phase or phase transition can emerge in a many-body system. We derive the topological partition functions that characterize the LSM constraints in spin systems with $G_s\times G_{int}$ symmetry, where $G_s$ is an arbitrary space group in one or two spatial dimensions, and $G_{int}$ is any internal symmetry whose projective representations are classified by $\mathbb{Z}_2^k$ with $k$ an integer. We then apply these results to study the emergibility of a class of exotic quantum critical states, including the well-known deconfined quantum critical point (DQCP), $U(1)$ Dirac spin liquid (DSL), and the recently proposed non-Lagrangian Stiefel liquid. These states can emerge as a consequence of the competition between a magnetic state and a non-magnetic state. We identify all possible realizations of these states on systems with $SO(3)\times \mathbb{Z}_2^T$ internal symmetry and either $p6m$ or $p4m$ lattice symmetry. Many interesting examples are discovered, including a DQCP adjacent to a ferromagnet, stable DSLs on square and honeycomb lattices, and a class of quantum critical spin-quadrupolar liquids of which the most relevant spinful fluctuations carry spin-$2$. In particular, there is a realization of spin-quadrupolar DSL that is beyond the usual parton construction. We further use our formalism to analyze the stability of these states under symmetry-breaking perturbations, such as spin-orbit coupling. As a concrete example, we find that a DSL can be stable in a recently proposed candidate material, NaYbO$_2$.

  18 citations