arXiv subjects

Tarun Grover

Publications and source records attributed to Tarun Grover.

At least 19 recordsLinked to original sources

arXiv2026

Dynamical splitting and a nodal Bose liquid in 2d chiral XYZ model

We study a class of Hamiltonians with a structure that we call "dynamical splitting": the Hamiltonian terms can be divided into two sets acting on the same degrees of freedom such that every term in one set commutes with every term in the other, although terms within either set do not all commute. This structure yields an algebraic duality to effective degrees of freedom on which the two parts of the Hamiltonian act disjointly, enabling exact diagonalization on lattices with approximately twice as many spins as usually accessible. We exploit it in the "chiral XYZ model", a geometrically frustrated spin-$1/2$ model on the triangular lattice which was previously introduced as a special limit of a Majorana-Hubbard model. This model also possesses anticommuting noncontractible line symmetries, which enforce an exact, topology-dependent degeneracy between locally indistinguishable states. We first study a $\mathbb{Z}_N$ clock generalization and find, at large $N$, a gapless ground state with three subsystem-symmetry-protected nodal lines. Exploiting dynamical splitting and the subsystem symmetries, we carry out exact diagonalization of the $N=2$ model on lattices up to $9\times9$ spins. The many-body gap and bipartite entanglement provide strong evidence for a gapless state consistent with the large-$N$ nodal structure: the entanglement scales as $L\log L$ and exhibits $1+1$-dimensional CFT-like chord scaling on cylinders. Finally, we study instabilities and proximate phases. In particular, we find evidence that a subsystem-symmetry-preserving deformation drives a finite coupling transition to a gapped phase with $\mathbb Z_2 \times \mathbb Z_2$ topological order.

cond-mat.str-el↗

arXiv2026

Hierarchical entanglement transitions and hidden area-law sectors in quantum many-body dynamics

Chaotic many-body dynamics typically generates volume-law entanglement from initially low-entangled states. We reveal an intricate, hierarchical entanglement structure in local quantum quenches, both in the canonical purification of locally quenched Gibbs states and in a companion pure-state circuit model. In either setting, the full state exhibits a Renyi-index-tuned transition: at long times, $S_{\alpha>1}$ obeys an area law, while $S_{\alpha\le 1}$ is volume-law. More strikingly, the response linear in the quench strength is carried by only an O(1)-dimensional dominant Schmidt sector; the corresponding states exhibit their own area-to-volume-law transitions at critical indices $\alpha_c<1$, implying polynomial-bond-dimension approximability in one dimension. We provide evidence that this hierarchy persists recursively: upon bipartitioning the dominant Schmidt states, their leading Schmidt sectors exhibit analogous structure. We derive the mechanism analytically in the circuit model, prove the $S_{\alpha>1}$ area law for locally quenched Gibbs states, and support the hierarchy by exact diagonalization of random circuits and locally quenched Gibbs states of chaotic spin chains.

quant-ph↗

arXiv2026

Non-perturbative constraints on stability and renormalization group flows in nonequilibrium matter

We derive constraints on renormalization group (RG) flows and stability of phases in nonequilibrium systems using quantum information inequalities. These constraints involve conditional mutual information (CMI), which quantifies correlations between spatially separated regions not mediated by their surroundings. First, assuming CMI is UV finite, we derive a monotonicity constraint on its crossover scaling function. Under certain assumptions, this implies that the CMI scaling exponent cannot increase along the RG flow. Second, we bound the CMI of a convex mixture of states in terms of the CMI of individual components. We use this inequality to infer perturbative stability of spontaneous symmetry breaking states against quantum channels that explicitly break symmetry. We illustrate these constraints through several examples, including decoherence-driven transitions in classical symmetry-broken states, area-law CMI in anisotropic conserved dynamics, and even transitions in pure quantum states. We also discuss implications for classical nonequilibrium steady states.

cond-mat.stat-mech↗

arXiv2025

Local Reversibility and Divergent Markov Length in 1+1-D Directed Percolation

Recent progress in open many-body quantum systems has highlighted the importance of the Markov length, the characteristic scale over which conditional correlations decay. It has been proposed that non-equilibrium phases of matter can be defined as equivalence classes of states connected by short-time evolution while maintaining a finite Markov length, a notion called local reversibility. A natural question is whether well-known classical models of non-equilibrium criticality fit within this framework. Here we investigate the Domany-Kinzel model -- which exhibits an active phase and an absorbing phase separated by a 1+1-D directed-percolation transition -- from this information-theoretic perspective. Using tensor network simulations, we provide evidence for local reversibility within the active phase. Notably, the Markov length diverges upon approaching the critical point, unlike classical equilibrium transitions where Markov length is zero due to their Gibbs character. Correspondingly, the conditional mutual information exhibits scaling consistent with directed percolation universality. Further, we analytically study the case of 1+1-D compact directed percolation, where the Markov length diverges throughout the phase diagram due to spontaneous breaking of domain-wall parity symmetry from strong to weak. Nevertheless, the conditional mutual information continues to faithfully detect the corresponding phase transition.

cond-mat.stat-mech↗

arXiv2025

Dimensionality-Changing Transition from a Non-Fermi Liquid to a Spin-Solid in a Multichannel Kondo Lattice

A multichannel Kondo system, where a single quantum spin couples to multiple channels of an electronic bath, provides one of the simplest examples of a zero-dimensional non-Fermi liquid. It is natural to ask: what happens when an extensive number of such systems are coupled together? A simple renormalization group argument implies that in a chain of SU(N) multichannel quantum systems, where each spin is coupled to its own bath of K channels, the individual spins dynamically decouple at low energy when N>K, resulting in a 'sliding' non-Fermi liquid. Using Quantum Monte Carlo (QMC) simulations, we find evidences of a continuous, 'dimensionality-changing' phase transition out of this non-Fermi liquid into a valence-bond solid phase as the intersite coupling is increased. Remarkably, at the critical point, correlations exhibit a power-law behavior even along the direction in which the spins are coupled, indicating the breakdown of dynamical decoupling at the transition. We also develop an RG scheme to understand the universal aspects of this transition.

cond-mat.str-el↗

arXiv2025

A Perturbative Approach to Symmetric Mass Generation

The Landau paradigm has been a powerful framework for understanding phase transitions involving spontaneous symmetry breaking. In contrast, phase transitions between two symmetric phases, where neither phase breaks any symmetry, remain less explored. One intriguing class of such transitions involves "symmetric mass generation" (SMG), where interactions drive a transition from a gapless symmetric phase to a gapped symmetric phase. In this work, we develop a controlled perturbative approach to study a class of such transitions, based on an $\epsilon$-expansion around the critical dimension where the SMG-inducing-interaction becomes marginal. Applying this method to two distinct models, we identify a single-parameter-tuned transition in each case, which we conjecture captures the universal critical behavior of the SMG transition in these models. We compute universal quantities associated with these transitions.

cond-mat.str-el↗

arXiv2025

Mixed-state phases from local reversibility

We propose a refined definition of mixed-state phase equivalence based on locally reversible channel circuits. We show that such circuits preserve topological degeneracy and the locality of all operators including both strong and weak symmetries. Under a locally reversible channel, weak unitary symmetries are locally dressed into channel symmetries, a new generalization of symmetry for open quantum systems. For abelian higher-form symmetries, we show the refined definition preserves anomalies and spontaneous breaking of such symmetries within a phase. As a primary example, a two-dimensional classical loop ensemble is trivial under the previously adopted definition of mixed-state phases. However, it has non-trivial topological degeneracy arising from a mutual anomaly between strong and weak 1-form symmetries, and our results show that it is not connected to a trivial state via locally reversible channel circuits.

quant-ph↗

arXiv2025

Analogs of deconfined quantum criticality for non-invertible symmetry breaking in 1d

The spontaneous breaking of non-invertible symmetries can lead to exotic phenomena such as coexistence of order and disorder. Here we explore second-order phase transitions in 1d spin chains between two phases that correspond to distinct patterns of non-invertible symmetry breaking. The critical point shares several features with well-understood examples of deconfined quantum critical points, such as enlarged symmetry and identical exponents for the two order parameters participating in the transition. Interestingly, such deconfined transitions involving non-invertible symmetries allow one to construct a whole family of similar critical points by gauging spin-flip symmetries. By employing gauging and bosonization, we characterize the phase diagram of our model in the vicinity of the critical point. We also explore proximate phases and phase transitions in related models, including a deconfined quantum critical point between invertible order parameters that is enforced by a non-invertible symmetry.

cond-mat.str-el↗

arXiv2025

A critical theory for solidification of a liquid Fermi liquid

We give a simple description of a zero-temperature phase transition between a liquid metal and a solid. The critical point has a Fermi surface as well as a Bose surface, a sphere in momentum space of gapless bosonic excitations. We find a fixed point of the renormalization group governing such a non-Fermi liquid, using an expansion in the codimension of both the Fermi and Bose surfaces. We comment on the nature of the solid phase and possible physical realizations.

cond-mat.str-el↗

arXiv2025

Zipping many-body quantum states: a scalable approach to diagonal entropy

The outcomes of projective measurements on a quantum many-body system in a chosen basis are inherently probabilistic. The Shannon entropy of this probability distribution (the "diagonal entropy") often reveals universal features, such as the existence of a quantum phase transition. A brute-force tomographic approach to estimating this entropy scales exponentially with the system size. Here, we explore using the Lempel-Ziv lossless image compression algorithm as an efficient, scalable alternative, readily implementable in a quantum gas microscope or programmable quantum devices. We test this approach on several examples: one-dimensional quantum Ising model, and two-dimensional states that display conventional symmetry breaking due to quantum fluctuations, or strong-to-weak symmetry-breaking due to local decoherence. We also employ the diagonal mixed state to put constraints on the phase boundaries of our models. In all examples, the compression method accurately recovers the entropy density while requiring at most polynomially many images. We also analyze the singular part of the diagonal entropy density using renormalization group on a replicated action. In the 1+1-D quantum Ising model, we find that it scales as $|t| \log|t|$, where $t$ is the deviation from the critical point, while in a 2+1-D state with amplitudes proportional to the Boltzmann weight of the 2D Ising model, it follows a $t^2 \log|t|$ scaling.

quant-ph↗

arXiv2024

An analog of topological entanglement entropy for mixed states

We propose the convex-roof extension of quantum conditional mutual information ("co(QCMI)") as a diagnostic of topological order in a mixed state. We focus primarily on topological states subjected to local decoherence, and employ the Levin-Wen scheme to define co(QCMI), so that for a pure state, co(QCMI) equals topological entanglement entropy (TEE). By construction, co(QCMI) is zero if and only if a mixed state can be decomposed as a convex sum of pure states with zero TEE. We show that co(QCMI) is non-increasing with increasing decoherence when Kraus operators are proportional to the product of onsite unitaries. This implies that unlike a pure state transition between a topologically trivial and a non-trivial phase, the long-range entanglement at a decoherence-induced topological phase transition as quantified by co(QCMI) is less than or equal to that in the proximate topological phase. For the 2d toric code decohered by onsite bit/phase-flip noise, we show that co(QCMI) is non-zero below the error-recovery threshold and zero above it. Relatedly, the decohered state cannot be written as a convex sum of short-range entangled pure states below the threshold. We conjecture and provide evidence that in this example, co(QCMI) equals TEE of a recently introduced pure state. In particular, we develop a tensor-assisted Monte Carlo (TMC) computation method to efficiently evaluate the R\'enyi TEE for the aforementioned pure state and provide non-trivial consistency checks for our conjecture. We use TMC to also calculate the universal scaling dimension of the anyon-condensation order parameter at this transition.

quant-ph↗

arXiv2024

Nishimori's self-tuning as evidence for the existence of God

Apparent violations of Naturalness may be explained by positing the existence of an omniscient but disinterested and possibly fallible Observer who regularly performs von Neumann measurements on us (and everything else). We comment briefly on the implications for the construction of scalable quantum computers.

hep-th↗

arXiv2024

Unconventional topological mixed-state transition and critical phase induced by self-dual coherent errors

A topological phase can undergo a phase transition driven by anyon condensation. A potential obstruction to such a mechanism could arise if there exists a symmetry between anyons that have non-trivial mutual statistics. Here we consider toric code subjected to errors that tend to proliferate anyons with non-trivial mutual statistics. Using triangle inequality, we show that in the presence of electromagnetic duality and a partial-transpose symmetry, a decoherence induced phase transition out of the topological phase must be rather unconventional and lie beyond standard rules of anyon condensation. To explore such physics, we first subject toric code to a self-dual quantum channel where Kraus operators are proportional to X+Z. We find that the topological phase is stable up to the maximal error rate, when viewing density matrix as a pure state in the double Hilbert space. To access an unconventional transition, we then consider a perturbed toric code subjected to the self-dual channel, and find numerical evidence that beyond a critical error rate, the topological phase is destroyed resulting in a critical phase where anyons are only power-law condensed.

quant-ph↗

arXiv2023

Symmetry-enforced many-body separability transitions

We study quantum many-body mixed states with a symmetry from the perspective of separability, i.e., whether a mixed state can be expressed as an ensemble of short-range entangled (SRE) symmetric pure states. We provide evidence for 'symmetry-enforced separability transitions' in a variety of states, where in one regime the mixed state is expressible as a convex sum of symmetric SRE pure states, while in the other regime, such a representation is not feasible. We first discuss Gibbs state of Hamiltonians that exhibit spontaneous breaking of a discrete symmetry, and argue that the associated thermal phase transition can be thought of as a symmetry-enforced separability transition. Next, we study cluster states in various dimensions subjected to local decoherence, and identify several distinct mixed-state phases and associated separability phase transitions, which also provides an alternate perspective on recently discussed 'average SPT order'. We also study decohered p+ip superconductors, and find that if the decoherence breaks the fermion parity explicitly, then the resulting mixed state can be expressed as a convex sum of non-chiral states, while a fermion-parity preserving decoherence results in a phase transition at a non-zero threshold that corresponds to spontaneous breaking of fermion parity. Finally, we briefly discuss systems that satisfy NLTS (no low-energy trivial state) property, such as the recently discovered good LDPC codes, and argue that the Gibbs state of such systems exhibits a temperature-tuned separability transition.

quant-ph↗

arXiv2023

Separability transitions in topological states induced by local decoherence

We study states with intrinsic topological order subjected to local decoherence from the perspective of separability, i.e., whether a decohered mixed state can be expressed as an ensemble of short-range entangled (SRE) pure states. We focus on toric codes and the X-cube fracton state and provide evidence for the existence of decoherence-induced separability transitions that precisely coincide with the threshold for the feasibility of active error correction. A key insight is that local decoherence acting on the 'parent' cluster states of these models results in a Gibbs state. As an example, for the 2d (3d) toric code subjected to bit-flip errors, we show that the decohered density matrix can be written as a convex sum of SRE states for $p > p_c$, where $p_c$ is related to the paramagnetic-ferromagnetic transition in the 2d (3d) random-field bond Ising model along the Nishimori line.

quant-ph↗

arXiv2023

Critical phase induced by Berry phase and dissipation in a spin chain

Motivated by experiments on spin chains embedded in a metallic bath, as well as closed quantum systems described by long-range interacting Hamiltonians, we study a critical SU(N) spin chain perturbed by dissipation, or equivalently, after space-time rotation, long-range spatial interactions. The interplay of dissipation and the Wess-Zumino (Berry phase) term results in a rich phase diagram with multiple renormalization-group fixed points. For a range of the exponent that characterizes the dissipative bath, we find a second-order phase transition between the fixed point that describes an isolated critical spin chain and a dissipation-induced-ordered phase. More interestingly, for a different range of the exponent, we find a stable, gapless, nonrelativistic phase of matter whose existence necessarily requires coupling to the dissipative bath. Upon tuning the exponent, we find that the fixed point corresponding to this gapless, stable phase "annihilates" the fixed point that describes the transition out of this phase to the ordered phase. We also study a relativistic version of our model, and we identify a new critical point. We discuss the implications of our work for Kondo lattice systems and engineered long-range interacting quantum systems.

cond-mat.str-el↗

arXiv2023

Fermionic skyrmions and bosonization for a Gross-Neveu transition

We investigate a 2+1-D interacting Dirac semimetal with onsite flavor SU(2) symmetry. Topological considerations imply that the skyrmions in the flavor-symmetry-breaking phase carry electron quantum numbers, motivating a dual bosonized low energy description in terms of two complex scalars coupled to an abelian Chern-Simons field. We propose that the transition between a nearby Chern insulator and the flavor symmetry-broken phase is a bicritical point in the bosonized description, and also suggest that the Gross-Neveu-Heisenberg (GNH) transition between the Dirac semimetal and the flavor symmetry-broken phase is a tricritical point. Heuristically, the dual description corresponds to the gap closing of fermionic skyrmions. We discuss implications and potential issues with our proposal, and motivated from it, perform extensive unbiased Determinantal Quantum Monte Carlo (DQMC) simulations on a lattice regularized Hamiltonian for the GNH transition, extending previously available results. We compare DQMC results with the estimates in the proposed dual from available perturbative renormalization group results. We also numerically demonstrate the presence of fermionic skyrmions in the symmetry-broken phase of our lattice model.

cond-mat.str-el↗

arXiv2022

Spin chain on a metallic surface: Dissipation-induced order vs. Kondo entanglement

We explore the physics of a spin-1/2 Heisenberg chain with Kondo interaction, $J_k$, to a two-dimensional electron gas. At weak $J_k$ the problem maps onto a Heisenberg chain locally coupled to a dissipative Ohmic bath. At the decoupled fixed point, the dissipation is a marginally relevant perturbation and drives long-range antiferromagnetic order along the chain. In the dynamical spin structure factor we observe a quadratic low-energy dispersion akin to Landau-damped Goldstone modes. At large $J_k$ Kondo screening dominates, and the spin correlations of the chain inherit the power law of the host metal, akin to a paramagnetic heavy Fermi liquid. In both phases we observe heavy bands near the Fermi energy in the composite-fermion spectral function. Our results, obtained from auxiliary-field quantum Monte Carlo simulations, provide a unique negative-sign-free realization of a quantum transition between an antiferromagnetic metal and a heavy-fermion metal. We discuss the relevance of our results in the context of scanning tunneling spectroscopy experiments of magnetic adatom chains on metallic surfaces.

cond-mat.str-el↗