arXiv subjects

G. Shankar

Publications and source records attributed to G. Shankar.

7 recordsLinked to original sources

arXiv2026

Lieb-Schultz-Mattis constraints for hyperbolic lattices

The Lieb-Schultz-Mattis (LSM) theorem and its higher-dimensional extensions forbid the existence of a unique, symmetric, and gapped ground state at fractional fillings in quantum many-body systems with a conserved particle number (or spin angular momentum) and the conventional translation symmetry of Euclidean lattices. In this work, we propose a generalization of the LSM theorem to quantum many-body systems on hyperbolic lattices, i.e., regular tessellations of two-dimensional negatively curved space. By leveraging concepts from hyperbolic band theory in a many-body setting, we adapt Oshikawa's flux-threading argument to periodic hyperbolic lattices with a non-Euclidean (Fuchsian) translation symmetry and compute a lower-bound to the ground-state degeneracy as a function of filling and lattice geometry. We explore the consequences of LSM constraints for gapped phases of hyperbolic quantum matter and suggest frustrated spin models on hyperbolic analogs of the square and triangular lattices as promising platforms for realizing symmetric spin liquids in hyperbolic space.

cond-mat.str-el↗

arXiv2023

Monopoles in Dirac spin liquids and their symmetries from instanton calculus

The Dirac spin liquid (DSL) is a two-dimensional (2D) fractionalized Mott insulator featuring massless Dirac spinon excitations coupled to a compact $U(1)$ gauge field, which allows for flux-tunneling instanton events described by magnetic monopoles in (2+1)D Euclidean spacetime. The state-operator correspondence of conformal field theory has been used recently to define associated monopole operators and determine their quantum numbers, which encode the microscopic symmetries of conventional ordered phases proximate to the DSL. In this work, we utilize semiclassical instanton methods not relying on conformal invariance to construct monopole operators directly in (2+1)D spacetime as instanton-induced 't Hooft vertices, i.e., fermion-number-violating effective interactions originating from zero modes of the Euclidean Dirac operator in an instanton background. In the presence of a flavor-adjoint fermion mass, resummation of the instanton gas is shown to select the correct monopole to be proliferated, in accordance with predictions of the state-operator correspondence. We also show that our instanton-based approach is able to determine monopole quantum numbers on bipartite lattices.

cond-mat.str-el↗

arXiv2023

Hyperbolic lattices and two-dimensional Yang-Mills theory

Hyperbolic lattices are a new type of synthetic quantum matter emulated in circuit quantum electrodynamics and electric-circuit networks, where particles coherently hop on a discrete tessellation of two-dimensional negatively curved space. While real-space methods and a reciprocal-space hyperbolic band theory have been recently proposed to analyze the energy spectra of those systems, discrepancies between the two sets of approaches remain. In this work, we reconcile those approaches by first establishing an equivalence between hyperbolic band theory and $U(N)$ topological Yang-Mills theory on higher-genus Riemann surfaces. We then show that moments of the density of states of hyperbolic tight-binding models correspond to expectation values of Wilson loops in the quantum gauge theory and become exact in the large-$N$ limit.

cond-mat.mes-hall↗

arXiv2022

Continuous transition between Ising magnetic order and a chiral spin liquid

The competition between fractionalized spin-liquid states and magnetically ordered phases is an important paradigm in frustrated magnetism. Spin-orbit coupled Mott insulators with Ising-like magnetic anisotropies, such as Kitaev materials, are a particularly rich playground to explore this competition. In this work, we use effective field theory methods to show that a direct quantum phase transition can occur in two-dimensional (2D) Ising spin systems between a topologically ordered chiral spin liquid and a phase with magnetic long-range order. Such a transition can be protected by lattice symmetries and is described by a theory of massless Majorana fields coupled to non-Abelian $SO(N)$ gauge fields with a Chern-Simons term. We further show that Euclidean Majorana zero modes bound to $\mathbb{Z}_2$ monopole-instantons in the emergent non-Abelian gauge field are key to understanding spontaneous symmetry breaking in the ordered phase.

cond-mat.str-el↗

arXiv2021

Symmetry-breaking effects of instantons in parton gauge theories

Compact quantum electrodynamics (CQED$_3$) with Dirac fermionic matter provides an adequate framework for elucidating the universal low-energy physics of a wide variety of (2+1)D strongly correlated systems. Fractionalized states of matter correspond to its deconfined phases, where the gauge field is effectively noncompact, while conventional broken-symmetry phases are associated with confinement triggered by the proliferation of monopole-instantons. While much attention has been devoted lately to the symmetry classification of monopole operators in massless CQED$_3$ and related 3D conformal field theories, explicit derivations of instanton dynamics in parton gauge theories with fermions have been lacking. In this work, we use semiclassical methods analogous to those used by 't Hooft in the solution of the $U(1)$ problem in 4D quantum chromodynamics (QCD) to explicitly demonstrate the symmetry-breaking effect of instantons in CQED$_3$ with massive fermions, motivated by a fermionic parton description of hard-core bosons on a lattice. By contrast with the massless case studied by Marston, we find that massive fermions possess Euclidean zero modes exponentially localized to the center of the instanton. Such Euclidean zero modes produce in turn an effective four-fermion interaction -- known as the 't Hooft vertex in QCD -- which naturally leads to two possible superfluid phases for the original microscopic bosons: a conventional single-particle condensate or an exotic boson pair condensate without single-particle condensation.

cond-mat.str-el↗

arXiv2019

Exactly solvable Majorana-Anderson impurity models

Motivated by recent experimental progress in the realization of hybrid structures with a topologically superconducting nanowire coupled to a quantum dot, viewed through the lens of the emerging field of correlated Majorana fermions, we introduce a class of interacting Majorana-Anderson impurity models which admit an exact solution for a wide range of parameters, including on-site repulsive interactions of arbitrary strength. The model is solved by mapping it via the $\mathbb{Z}_2$ slave-spin method to a noninteracting resonant level model for auxiliary Majorana degrees of freedom. The resulting gauge constraint is eliminated by exploiting the transformation properties of the Hamiltonian under a special local particle-hole transformation. For a spin-polarized Kitaev chain coupled to a quantum dot, we obtain exact expressions for the dot spectral functions at both zero and finite temperature. We study how the interaction strength and localization length of the end Majorana zero mode affect physical properties of the dot, such as quasiparticle weight, double occupancy, and odd-frequency pairing correlations, as well as the local electronic density of states in the superconducting chain.

cond-mat.str-el↗

arXiv2012

Innovative SQA Service Maturity Model using CMMI and ITIL

This Journal details a maturity model for SQA services which has been developed during QMS implementation in the IT division of a large multinational organization. The scope of the engagement was to establish a standard set of processes based on CMMI\textregistered and ITIL\textregistered Framework across four business verticals scattered in Europe, United States and Asia. The services of Software Quality Analyst (SQA) from different vendors were leveraged to facilitate implementation of processes which was referred to as the Quality Management System (QMS). To co-ordinate and support QMS implementation, a Software Quality Assurance Group (SQAG) was established at the organizational level. Considering the large number of applications, the business verticals proposed that process implementation should be owned and managed by practitioners themselves so that the mass deployment of QMS can be achieved at a faster rate with the same SQA capacity. This called for a need to devise an innovative implementation solution before moving to a process implementation model which proposed Project Managers implementing processes themself. While there are process models and frameworks available in the market for establishing processes in an organization, there is no model that elaborates activities to be performed by the SQA for effective implementation of processes. SQA service maturity model was proposed as a solution based on CMMI\textregistered and developed to eventually proceed towards a 'Process Implementation Model proposing Project Managers implementing processes themself'. SQA Service Maturity Model is a Software Quality Assurance implementation framework that enables organisations to increase Efficiencies in Software Quality Assurance, reduce the Cost of Defects and ultimately Increasing Return on Investment in IT.

cs.OH↗