arXiv subjects

Arkya Chatterjee

Publications and source records attributed to Arkya Chatterjee.

12 recordsLinked to original sources

arXiv2026

Generalized Kramers-Wannier Self-Duality in Hopf-Ising Models

The Kramers-Wannier transformation of the 1+1d transverse-field Ising model exchanges the paramagnetic and ferromagnetic phases and, at criticality, manifests as a non-invertible symmetry. Extending such self-duality symmetries beyond gauging of abelian groups in tensor-product Hilbert spaces has, however, remained challenging. In this work, we construct a generalized 1+1d Ising model based on a finite-dimensional semisimple Hopf algebra $H$ that enjoys an anomaly-free non-invertible symmetry $\mathrm{Rep}(H)$. We provide an intuitive diagrammatic formulation of both the Hamiltonian and the symmetry operators using a non-(co)commutative generalization of ZX-calculus built from Hopf-algebraic data. When $H$ is self-dual, we further construct a generalized Kramers-Wannier duality operator that exchanges the paramagnetic and ferromagnetic phases and becomes a non-invertible symmetry at the self-dual point. This enlarged symmetry mixes with lattice translation and, in the infrared, flows to a weakly integral fusion category given by a $\mathbb{Z}_2$ extension of $\mathrm{Rep}(H)$. Specializing to the Kac-Paljutkin algebra $H_8$, the smallest self-dual Hopf algebra beyond abelian group algebras, we numerically study the phase diagram and identify four of the six $\mathrm{Rep}(H_8)$-symmetric gapped phases, separated by Ising critical lines and meeting at a multicritical point. We also realize all six $\mathrm{Rep}(H_8)$-symmetric gapped phases on the lattice via the $H$-comodule algebra formalism, in agreement with the module-category classification of $\mathrm{Rep}(H_8)$. Our results provide a unified Hopf-algebraic framework for non-invertible symmetries, dualities, and the tensor product lattice models that realize them.

cond-mat.str-el↗

arXiv2025

Parity anomaly from LSM: exact valley symmetries on the lattice

We show that the honeycomb tight-binding model hosts an exact microscopic avatar of its low-energy SU(2) valley symmetry and parity anomaly. Specifically, the SU(2) valley symmetry arises from a collection of conserved, integer quantized charge operators that obey the Onsager algebra. Along with lattice reflection and time-reversal symmetries, this Onsager symmetry has a Lieb-Schultz-Mattis (LSM) anomaly that matches the parity anomaly in the IR. Indeed, we show that any local Hamiltonian commuting with these symmetries cannot have a trivial unique gapped ground state. We study the phase diagram of the simplest symmetric model and survey various deformations, including Haldane's mass term, which preserves only the Onsager symmetry. Our results place the parity anomaly in ${2+1}$D alongside Schwinger's anomaly in ${1+1}$D and Witten's SU(2) anomaly in ${3+1}$D as 't Hooft anomalies that can arise from the Onsager symmetry on the lattice.

cond-mat.str-el↗

arXiv2024

Lattice T-duality from non-invertible symmetries in quantum spin chains

Dualities of quantum field theories are challenging to realize in lattice models of qubits. In this work, we explore one of the simplest dualities, T-duality of the compact boson CFT, and its realization in quantum spin chains. In the special case of the XX model, we uncover an exact lattice T-duality, which is associated with a non-invertible symmetry that exchanges two lattice U(1) symmetries. The latter symmetries flow to the momentum and winding U(1) symmetries with a mixed anomaly in the CFT. However, the charge operators of the two U(1) symmetries do not commute on the lattice and instead generate the Onsager algebra. We discuss how some of the anomalies in the CFT are nonetheless still exactly realized on the lattice and how the lattice U(1) symmetries enforce gaplessness. We further explore lattice deformations preserving both U(1) symmetries and find a rich gapless phase diagram with special $\mathrm{Spin}(2k)_1$ WZW model points and whose phase transitions all have dynamical exponent ${z>1}$.

cond-mat.str-el↗

arXiv2024

Quantized axial charge of staggered fermions and the chiral anomaly

In the 1+1D ultra-local lattice Hamiltonian for staggered fermions with a finite-dimensional Hilbert space, there are two conserved, integer-valued charges that flow in the continuum limit to the vector and axial charges of a massless Dirac fermion with a perturbative anomaly. Each of the two lattice charges generates an ordinary U(1) global symmetry that acts locally on operators and can be gauged individually. Interestingly, they do not commute on a finite lattice and generate the Onsager algebra, but their commutator goes to zero in the continuum limit. The chiral anomaly is matched by this non-abelian algebra, which is consistent with the Nielsen-Ninomiya theorem. We further prove that the presence of these two conserved lattice charges forces the low-energy phase to be gapless, reminiscent of the consequence from perturbative anomalies of continuous global symmetries in continuum field theory. Upon bosonization, these two charges lead to two exact U(1) symmetries in the XX model that flow to the momentum and winding symmetries in the free boson conformal field theory.

hep-th↗

arXiv2024

Analytic framework for self-dual criticality in $\mathbb{Z}_k$ gauge theory with matter

The deconfined phase of 2+1D $\mathbb{Z}_k$ gauge theory exhibits topological order, with $e$ and $m$ anyons that have a $2\pi/k$ braiding phase. Proliferating either $e$ or $m$ drives Higgs or confinement transitions, respectively. At the multicritical point where these transitions meet, the theory enjoys an additional duality symmetry that exchanges $e$ and $m$ anyons. This symmetry forces anyons with nontrivial braiding to close their gaps simultaneously, giving rise to a critical theory that mixes strong interactions with mutual statistics. We propose an effective ${\rm U(1)}\times {\rm U(1)}$ gauge theory with a mutual Chern-Simons term at level $k$ to describe the vicinity of the multicritical point for $k \geq 4$. The emergence of a global ${\rm U(1)}^{\rm{top}} \times {\rm U(1)}^{\rm{top}}$ symmetry at the critical point imposes powerful constraints on universal properties of the phase transition. In particular, we show that (1) the lattice magnetic flux operator embeds as a conserved ${\rm U(1)}$ current with protected scaling dimension; (2) the first-order line emanating from the critical point for $k = 2$ disappears generically for sufficiently large $k$; (3) the correlation length exponent approaches that of the 3D XY model with corrections of order $1/k^2$ in the large $k$ limit. These predictions can be tested in near-term numerical simulations and pave the way for a more general exploration of topological quantum criticality enriched with anyon-permuting symmetries.

cond-mat.str-el↗

arXiv2024

Quantum Phases and Transitions in Spin Chains with Non-Invertible Symmetries

Generalized symmetries often appear in the form of emergent symmetries in low energy effective descriptions of quantum many-body systems. Non-invertible symmetries are a particularly exotic class of generalized symmetries, in that they are implemented by transformations that do not form a group. Such symmetries appear in large families of gapless states of quantum matter and constrain their low-energy dynamics. To provide a UV-complete description of such symmetries, it is useful to construct lattice models that respect these symmetries exactly. In this paper, we discuss two families of one-dimensional lattice Hamiltonians with finite on-site Hilbert spaces: one with (invertible) $S^{\,}_3$ symmetry and the other with non-invertible $\mathsf{Rep}(S^{\,}_3)$ symmetry. Our models are largely analytically tractable and demonstrate all possible spontaneous symmetry breaking patterns of these symmetries. Moreover, we use numerical techniques to study the nature of continuous phase transitions between the different symmetry-breaking gapped phases associated with both symmetries. Both models have self-dual lines, where the models are enriched by so-called intrinsically non-invertible symmetries generated by Kramers-Wannier-like duality transformations. We provide explicit lattice operators that generate these non-invertible self-duality symmetries. We show that the enhanced symmetry at the self-dual lines is described by a 2+1D symmetry-topological-order (SymTO) of type $\mathrm{JK}^{\,}_4\boxtimes \overline{\mathrm{JK}}^{\,}_4$. The condensable algebras of the SymTO determine the allowed gapped and gapless states of the self-dual $S^{\,}_3$-symmetric and $\mathsf{Rep}(S^{\,}_3)$-symmetric models.

cond-mat.str-el↗

arXiv2024

Implementing a synthetic magnetic vector potential in a 2D superconducting qubit array

Superconducting quantum processors are a compelling platform for analog quantum simulation due to the precision control, fast operation, and site-resolved readout inherent to the hardware. Arrays of coupled superconducting qubits natively emulate the dynamics of interacting particles according to the Bose-Hubbard model. However, many interesting condensed-matter phenomena emerge only in the presence of electromagnetic fields. Here, we emulate the dynamics of charged particles in an electromagnetic field using a superconducting quantum simulator. We realize a broadly adjustable synthetic magnetic vector potential by applying continuous modulation tones to all qubits. We verify that the synthetic vector potential obeys requisite properties of electromagnetism: a spatially-varying vector potential breaks time-reversal symmetry and generates a gauge-invariant synthetic magnetic field, and a temporally-varying vector potential produces a synthetic electric field. We demonstrate that the Hall effect--the transverse deflection of a charged particle propagating in an electromagnetic field--exists in the presence of the synthetic electromagnetic field.

quant-ph↗

arXiv2022

Emergent generalized symmetry and maximal symmetry-topological-order

A characteristic property of a gapless liquid state is its emergent symmetry and dual symmetry, associated with the conservation laws of symmetry charges and symmetry defects respectively. These conservation laws, considered on an equal footing, can't be described simply by the representation theory of a group (or a higher group). They are best described in terms of a topological order (TO) with gappable boundary in one higher dimension; we call this the symTO of the gapless state. The symTO can thus be considered a fingerprint of the gapless state. We propose that a largely complete characterization of a gapless state, up to local-low-energy equivalence, can be obtained in terms of its maximal emergent symTO. In this paper, we review the symmetry/topological-order (Symm/TO) correspondence and propose a precise definition of maximal symTO. We discuss various examples to illustrate these ideas. We find that the 1+1D Ising critical point has a maximal symTO described by the 2+1D double-Ising topological order. We provide a derivation of this result using symmetry twists in an exactly solvable model of the Ising critical point. The critical point in the 3-state Potts model has a maximal symTO of double (6,5)-minimal-model topological order. As an example of a noninvertible symmetry in 1+1D, we study the possible gapless states of a Fibonacci anyon chain with emergent double-Fibonacci symTO. We find the Fibonacci-anyon chain without translation symmetry has a critical point with unbroken double-Fibonacci symTO. In fact, such a critical theory has a maximal symTO of double (5,4)-minimal-model topological order. We argue that, in the presence of translation symmetry, the above critical point becomes a stable gapless phase with no symmetric relevant operator.

cond-mat.str-el↗

arXiv2022

Holographic theory for continuous phase transitions -- the emergence and symmetry protection of gaplessness

Two global symmetries are holo-equivalent if their algebras of local symmetric operators are isomorphic. Holo-equivalent classes of global symmetries are classified by gappable-boundary topological orders (TO) in one higher dimension (called symmetry TO), which leads to a symmetry/topological-order (Symm/TO) correspondence. We establish that: (1) For systems with a symmetry described by symmetry TO $M$, their gapped and gapless states are classified by condensable algebras $A$, formed by elementary excitations in $M$ with trivial self/mutual statistics. Such classified states (called $A$-states) can describe symmetry breaking orders, symmetry protected topological orders, symmetry enriched topological orders, gapless critical points, etc., in a unified way. (2) The local low-energy properties of an $A$-state can be calculated from its reduced symmetry TO $M_{/A}$, using holographic modular bootstrap (holoMB) which takes $M_{/A}$ as an input. Here $M_{/A}$ is obtained from $M$ by condensing excitations in $A$. Notably, an $A$-state must be gapless if $M_{/A}$ is nontrivial. This provides a unified understanding of the emergence and symmetry protection of gaplessness that applies to symmetries that are anomalous, higher-form, and/or non-invertible. (3) The relations between condensable algebras constrain the structure of the global phase diagram. (4) 1+1D bosonic systems with $S_3$ symmetry have four gapped phases with unbroken symmetries $S_3$, $\mathbb{Z}_3$, $\mathbb{Z}_2$, and $\mathbb{Z}_1$. We find a duality between two transitions $S_3 \leftrightarrow \mathbb{Z}_1$ and $\mathbb{Z}_3 \leftrightarrow \mathbb{Z}_2$: they are either both first order or both (stably) continuous, and in the latter case, they are described by the same conformal field theory (CFT).

cond-mat.str-el↗

arXiv2022

Symmetry as a shadow of topological order and a derivation of topological holographic principle

Symmetry is usually defined via transformations described by a (higher) group. But a symmetry really corresponds to an algebra of local symmetric operators, which directly constrains the properties of the system. In this paper, we point out that the algebra of local symmetric operators contains a special class of extended operators -- transparent patch operators, which reveal the selection sectors and hence the corresponding symmetry. The algebra of those transparent patch operators in $n$-dimensional space gives rise to a non-degenerate braided fusion $n$-category, which happens to describe a topological order in one higher dimension (for finite symmetry). Such a holographic theory not only describes (higher) symmetries, it also describes anomalous (higher) symmetries, non-invertible (higher) symmetries (also known as algebraic higher symmetries), and non-invertible gravitational anomalies. Thus, topological order in one higher dimension, replacing group, provides a unified and systematic description of the above generalized symmetries. This is referred to symmetry/topological-order (Symm/TO) correspondence. Our approach also leads to a derivation of topological holographic principle: \emph{boundary uniquely determines the bulk}, or more precisely, the algebra of local boundary operators uniquely determines the bulk topological order. As an application of the Symm/TO correspondence, we show the equivalence between $\mathbb{Z}_2\times \mathbb{Z}_2$ symmetry with mixed anomaly and $\mathbb{Z}_4$ symmetry, as well as between many other symmetries, in 1-dimensional space.

cond-mat.str-el↗

arXiv2022

Dynamics and stability of contractile actomyosin ring in the cell

Contraction of the cytokinetic ring during cell division leads to physical partitioning of a eukaryotic cell into two daughter cells. This involves flows of actin filaments and myosin motors in the growing membrane interface at the mid-plane of the dividing cell. Assuming boundary driven alignment of the acto-myosin filaments at the inner edge of the iterface we explore how the resulting active stresses influence the flow. Using the continuum gel theory framework, we obtain exact axisymmetric solutions of the dynamical equations. These solutions are consistent with experimental observations on closure rate. Using these solutions we perform linear stability analysis for the contracting ring under non-axisymmetric deformations. Our analysis shows that few low wave number modes, which are unstable during onset of the constriction, later on become stable when the ring shrinks to smaller radii, which is a generic feature of actomyosin ring closure. Our theory also captures how the effective tension in the ring decreases with its radius causing significant slow down in the contraction process at later times.

physics.bio-ph↗

arXiv2018

Aggregation and sedimentation of active Brownian particles at constant affinity

We study the motility-induced phase separation of active particles driven through the interconversion of two chemical species controlled by ideal reservoirs (chemiostats). As a consequence, the propulsion speed is non-constant and depends on the actual inter-particle forces, enhancing the positive feedback between increased density and reduced motility that is responsible for the observed inhomogeneous density. For hard discs, we find that this effect is negligible and that the phase separation is controlled by the average propulsion speed. For soft particles and large propulsion speeds, however, we predict an observable impact on the collective behavior. We briefly comment on the reentrant behavior found for soft discs. Finally, we study the influence of non-constant propulsion on the sedimentation profile of non-interacting active particles.

cond-mat.stat-mech↗