Carolyn Zhang
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View article: Non-invertible bosonic chiral symmetry on the lattice
Non-invertible bosonic chiral symmetry on the lattice Open
In this work we realize the 3 + 1 dimensional non-invertible ${\mathbb{Z}}_N$ chiral symmetry generator as an operator in a many body lattice Hilbert space. A crucial ingredient in our construction is the use of infinite dimensional $U(1)$…
View article: Lieb-Robinson Bounds with Exponential-in-Volume Tails
Lieb-Robinson Bounds with Exponential-in-Volume Tails Open
Lieb-Robinson bounds demonstrate the emergence of locality in many-body quantum systems. Intuitively, Lieb-Robinson bounds state that, with local or exponentially decaying interactions, the correlation that can be built up between two site…
View article: SymTFT Approach for Mixed States with Non-Invertible Symmetries
SymTFT Approach for Mixed States with Non-Invertible Symmetries Open
We develop a general framework for studying phases of mixed states with strong and weak symmetries, including non-invertible or categorical symmetries. The central idea is to consider a purification of the mixed state density matrix, which…
View article: Doping lattice non-abelian quantum Hall states
Doping lattice non-abelian quantum Hall states Open
We study quantum phases of a fluid of mobile charged non-abelian anyons, which arise upon doping the lattice Moore-Read quantum Hall state at lattice filling $ν= 1/2$ and its generalizations to the Read-Rezayi ($\mathrm{RR}_k$) sequence at…
View article: Enforced Gaplessness from States with Exponentially Decaying Correlations
Enforced Gaplessness from States with Exponentially Decaying Correlations Open
It is well known that an exponentially localized Hamiltonian must be gapless if its ground state has algebraic correlations. We show that even certain exponentially decaying correlations can imply gaplessness. This is exemplified by the de…
View article: Anomalies of Coset Non-Invertible Symmetries
Anomalies of Coset Non-Invertible Symmetries Open
Anomalies of global symmetries provide important information on the quantum dynamics. We show the dynamical constraints can be organized into three classes: genuine anomalies, fractional topological responses, and integer responses that ca…
View article: Lieb-Robinson bounds with exponential-in-volume tails
Lieb-Robinson bounds with exponential-in-volume tails Open
Lieb-Robinson bounds demonstrate the emergence of locality in many-body quantum systems. Intuitively, Lieb-Robinson bounds state that with local or exponentially decaying interactions, the correlation that can be built up between two sites…
View article: Anomalies of non-invertible symmetries in (3+1)d
Anomalies of non-invertible symmetries in (3+1)d Open
Anomalies of global symmetries are important tools for understanding the dynamics of quantum systems. We investigate anomalies of non-invertible symmetries in 3+1d using 4+1d bulk topological quantum field theories given by Abelian two-for…
View article: Fractionalization of coset non-invertible symmetry and exotic Hall conductance
Fractionalization of coset non-invertible symmetry and exotic Hall conductance Open
We investigate fractionalization of non-invertible symmetry in (2+1)D topological orders. We focus on coset non-invertible symmetries obtained by gauging non-normal subgroups of invertible 0 -form symmetries. These symmetries can arise a…
View article: Strong-to-weak spontaneous breaking of 1-form symmetry and intrinsically mixed topological order
Strong-to-weak spontaneous breaking of 1-form symmetry and intrinsically mixed topological order Open
Topological orders in 2+1d are spontaneous symmetry-breaking (SSB) phases of 1-form symmetries in pure states. The notion of symmetry is further enriched in the context of mixed states, where a symmetry can be either ``strong" or ``weak". …
View article: Thermalization rates and quantum Ruelle-Pollicott resonances: insights from operator hydrodynamics
Thermalization rates and quantum Ruelle-Pollicott resonances: insights from operator hydrodynamics Open
In thermalizing many-body quantum systems without conservation laws such as ergodic Floquet and random unitary circuits, local expectation values are predicted to decay to their equilibrium values exponentially quickly. In this work we der…
View article: Anomalies of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>-dimensional categorical symmetries
Anomalies of -dimensional categorical symmetries Open
We present a general approach for detecting when a fusion category symmetry is anomalous, based on the existence of a special kind of Lagrangian algebra of the corresponding Drinfeld center. The Drinfeld center of a fusion category $\mathc…
View article: Hierarchy construction for non-abelian fractional quantum Hall states via anyon condensation
Hierarchy construction for non-abelian fractional quantum Hall states via anyon condensation Open
For a given parent fractional quantum Hall (FQH) state at filling fraction $ν$, the hierarchy construction produces FQH states at nearby filling fractions $\{ν_n\}$ by condensing minimally charged quasiholes or quasiparticles of the parent…
View article: Fractionalization of Coset Non-Invertible Symmetry and Exotic Hall Conductance
Fractionalization of Coset Non-Invertible Symmetry and Exotic Hall Conductance Open
We investigate fractionalization of non-invertible symmetry in (2+1)D topological orders. We focus on coset non-invertible symmetries obtained by gauging non-normal subgroups of invertible $0$-form symmetries. These symmetries can arise as…
View article: Bulk-Boundary Correspondence for Interacting Floquet Systems in Two Dimensions
Bulk-Boundary Correspondence for Interacting Floquet Systems in Two Dimensions Open
We present a method for deriving bulk and edge invariants for interacting, many-body localized Floquet systems in two spatial dimensions. This method is based on a general mathematical object which we call a flow. As an application of our …
View article: Anomalies of Non-Invertible Symmetries in (3+1)d
Anomalies of Non-Invertible Symmetries in (3+1)d Open
Anomalies of global symmetries are important tools for understanding the dynamics of quantum systems. We investigate anomalies of non-invertible symmetries in 3+1d using 4+1d bulk topological quantum field theories given by Abelian two-for…
View article: Antiunitary symmetry breaking and a hierarchy of purification transitions in Floquet non-unitary circuits
Antiunitary symmetry breaking and a hierarchy of purification transitions in Floquet non-unitary circuits Open
We consider how a maximally mixed state evolves under $(1+1)D$ Floquet non-unitary circuits with an antiunitary symmetry that squares to identity, that serves as a generalized $\mathcal{PT}$ symmetry. Upon tuning a parameter, the effective…
View article: Note on quantum cellular automata and strong equivalence
Note on quantum cellular automata and strong equivalence Open
In this note, we present some results on the classification of quantum cellular automata (QCA) in 1D under strong equivalence rather than stable equivalence. Under strong equivalence, we only allow adding ancillas carrying the original on-…
View article: Anomalies of $(1+1)D$ categorical symmetries
Anomalies of $(1+1)D$ categorical symmetries Open
We present a general approach for detecting when a fusion category symmetry is anomalous, based on the existence of a special kind of Lagrangian algebra of the corresponding Drinfeld center. The Drinfeld center of a fusion category $\mathc…
View article: Volume-law to area-law entanglement transition in a non-unitary periodic Gaussian circuit
Volume-law to area-law entanglement transition in a non-unitary periodic Gaussian circuit Open
We consider Gaussian quantum circuits that alternate unitary gates and post-selected weak measurements, with spatial translation symmetry and time periodicity. We show analytically that such models can host different kinds of measurement-i…
View article: Topological invariants for SPT entanglers
Topological invariants for SPT entanglers Open
We develop a framework for classifying locality preserving unitaries (LPUs) with internal, unitary symmetries in $d$ dimensions, based on $(d-1)$ dimensional ``flux insertion operators" which are easily computed from the unitary. Using thi…
View article: Bulk-boundary correspondence for interacting Floquet systems in two dimensions
Bulk-boundary correspondence for interacting Floquet systems in two dimensions Open
We present a method for deriving bulk and edge invariants for interacting, many-body localized Floquet systems in two spatial dimensions. This method is based on a general mathematical object which we call a flow. As an application of our …
View article: Exactly solvable model for a deconfined quantum critical point in 1D
Exactly solvable model for a deconfined quantum critical point in 1D Open
We construct an exactly solvable lattice model for a deconfined quantum critical point (DQCP) in (1+1) dimensions. This DQCP occurs in an unusual setting, namely at the edge of a (2+1) dimensional bosonic symmetry protected topological pha…
View article: Proposal for realizing anomalous Floquet insulators via Chern band annihilation
Proposal for realizing anomalous Floquet insulators via Chern band annihilation Open
Two-dimensional periodically driven systems can host an unconventional topological phase unattainable for equilibrium systems, termed the Anomalous Floquet-Anderson insulator (AFAI). The AFAI features a quasi-energy spectrum with chiral ed…
View article: Vanishing Hall conductance for commuting Hamiltonians
Vanishing Hall conductance for commuting Hamiltonians Open
We consider the process of flux insertion for ground states of almost local commuting projector Hamiltonians in two spatial dimensions. In the case of finite dimensional local Hilbert spaces, we prove that this process cannot pump any char…
View article: Report on 2108.01708v2
Report on 2108.01708v2 Open
Two-dimensional periodically driven systems can host an unconventional topological phase unattainable for equilibrium systems, termed the Anomalous Floquet-Anderson insulator (AFAI).The AFAI features a quasi-energy spectrum with chiral edg…
View article: Report on 2108.01708v2
Report on 2108.01708v2 Open
Two-dimensional periodically driven systems can host an unconventional topological phase unattainable for equilibrium systems, termed the Anomalous Floquet-Anderson insulator (AFAI).The AFAI features a quasi-energy spectrum with chiral edg…
View article: Realizing anomalous Floquet insulators via Chern band annihilation
Realizing anomalous Floquet insulators via Chern band annihilation Open
Two-dimensional periodically driven systems can host an unconventional topological phase unattainable for equilibrium systems, termed the Anomalous Floquet-Anderson insulator (AFAI). The AFAI features a quasi-energy spectrum with chiral ed…
View article: Classification of interacting Floquet phases with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>U</mml:mi><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math> symmetry in two dimensions
Classification of interacting Floquet phases with symmetry in two dimensions Open
We derive a complete classification of Floquet phases of interacting bosons\nand fermions with $U(1)$ symmetry in two spatial dimensions. According to our\nclassification, there is a one-to-one correspondence between these Floquet\nphases …
View article: Temporal encoding of bacterial identity and traits in growth dynamics
Temporal encoding of bacterial identity and traits in growth dynamics Open
Significance Microbiology has traditionally been defined by the study of the phenotypic traits of microorganisms. While some traits can be easily explained with a direct genetic basis, most are a result of complex interactions between the …