arXiv subjects

Ruochen Ma

Publications and source records attributed to Ruochen Ma.

14 recordsLinked to original sources

arXiv2026

Statistical Mechanics of Non-Abelian Learnability Transitions

Monitored many-body quantum systems can undergo sharp learnability transitions characterized by how much information can be learned by the observer. When the dynamics conserves a non-Abelian charge, such as an $SU(2)$ spin, understanding how the observer learns the total charge remains an outstanding problem. Unlike the Abelian case, where charge measurements on distinct sites commute, the $SU(2)$-symmetric readouts are noncommuting fusion measurements, making learning a genuinely quantum inference problem. In this work, we propose a theory of $1+1d$ monitored quantum dynamics with $SU(2)$ symmetry, and show that it can be described by an effective replicated loop model comprised of a replica-pairing field and a diffusive ($z=2$) background sector that carries the $SU(2)$ charge and remains gapless throughout the phase diagram. Our theory predicts that the "spin-sharpening'' and entanglement transitions coincide as a single transition. Ordering of the pairing field produces volume-law entanglement and hides the background sector from measurements, leading to a learning time of $t\sim L^{3}$ for the total spin. When the pairing field disorders, the background sector alone gives logarithmic entanglement and a diffusive learning time $t\sim L^{2}$. Our analysis is controlled by a large-loop-fugacity expansion.

quant-ph↗

arXiv2026

Average Categorical Symmetries in One-Dimensional Disordered Systems

We study one-dimensional disordered systems with average non-invertible symmetries, where quenched disorder may locally break part of the symmetry while preserving it upon disorder averaging. A canonical example is the random transverse-field Ising model, which at criticality exhibits an average Kramers-Wannier duality. We consider the general setting in which the full symmetry is described by a $G$-graded fusion category $\mathcal{B}$, whose identity component $\mathcal{A}$ remains exact, while the components with nontrivial $G$-grading are realized either exactly or only on average. We develop a topological holographic framework that encodes the symmetry data of the 1D system in a 2D topological order $\mathcal{Z}[\mathcal{A}]$ (the Drinfeld center of $\mathcal{A}$), enriched by an exact or, respectively, average $G$ symmetry. Within this framework, we obtain a complete classification of anomalies and average symmetry-protected topological (SPT) phases: when the components with nontrivial $G$-grading are realized only on average, the symmetry is anomaly-free if and only if $\mathcal{Z}[\mathcal{A}]$ admits a magnetic Lagrangian algebra that is invariant under the permutation action of $G$ on anyons. When an anomaly is present, we show that the ground state of a single disorder realization is long-range entangled with probability one in the thermodynamic limit, and is expected to exhibit power-law Griffiths singularities in the low-energy spectrum. Finally, we present an explicit, exactly solvable lattice model based on a symmetry-enriched string-net construction. It yields trivial ground state ensemble in the anomaly-free case, and exhibits exotic low-energy behavior in the presence of an average anomaly.

cond-mat.dis-nn↗

arXiv2025

Circuit-based characterization of finite-temperature quantum phases and self-correcting quantum memory

Quantum phases at zero temperature can be characterized as equivalence classes under local unitary transformations: two ground states within a gapped phase can be transformed into each other via a local unitary circuit. We generalize this circuit-based characterization of phases to systems at finite-temperature thermal equilibrium described by Gibbs states. We construct a channel circuit that approximately transforms one Gibbs state into another provided the two are connected by a path in parameter space along which a certain correlation-decay condition holds. For finite-dimensional systems of linear size $L$ and approximation error $\epsilon$, the locality of the circuit is ${\rm polylog}({\rm poly}(L)/\epsilon)$. The correlation-decay condition, which we specify, is expected to be satisfied in the interior of many noncritical thermal phases, including those displaying discrete symmetry breaking and topological order. As an application, we show that any system in the same thermal phase as a zero-temperature topological code coherently preserves quantum information for a macroscopically long time, establishing self-correction as a universal property of thermal phases. As part of the proof, we provide explicit encoding and decoding channel circuits to encode information into, and decode it from, a system in thermal equilibrium.

quant-ph↗

arXiv2024

Quantum Cellular Automata on Symmetric Subalgebras

We investigate quantum cellular automata (QCA) on one-dimensional spin systems defined over a subalgebra of the full local operator algebra - the symmetric subalgebra under a finite Abelian group symmetry $G$. For systems where each site carries a regular representation of $G$, we establish a complete classification of such subalgebra QCAs based on two topological invariants: (1) a surjective homomorphism from the group of subalgebra QCAs to the group of anyon permutation symmetries in a $(2+1)d$ $G$ gauge theory; and (2) a generalization of the Gross-Nesme-Vogts-Werner (GNVW) index that characterizes the flow of the symmetric subalgebra. Specifically, two subalgebra QCAs correspond to the same anyon permutation and share the same index if and only if they differ by a finite-depth unitary circuit composed of $G$-symmetric local gates. We also identify a set of operations that generate all subalgebra QCAs through finite compositions. As an example, we examine the Kramers-Wannier duality on a $\mathbb{Z}_2$ symmetric subalgebra, demonstrating that it maps to the $e$-$m$ permutation in the two-dimensional toric code and has an irrational index of $\sqrt{2}$. Therefore, it cannot be extended to a QCA over the full local operator algebra and mixes nontrivially with lattice translations.

quant-ph↗

arXiv2024

Lieb-Schultz-Mattis Theorem with Long-Range Interactions

We prove the Lieb-Schultz-Mattis theorem in $d$-dimensional spin systems exhibiting $SO(3)$ spin rotation and lattice translation symmetries in the presence of $k-$local interactions decaying as $\sim 1/r^\alpha$ with distance $r$. Two types of Hamiltonians are considered: Type I comprises long-range spin-spin couplings, while Type II features long-range couplings between $SO(3)$ symmetric local operators. For spin-$\frac{1}{2}$ systems, it is shown that Type I cannot have a unique symmetric ground state with a nonzero excitation gap when the interaction decays sufficiently fast, \ie when $\alpha>\max(3d,4d-2)$. For Type II, the condition becomes $\alpha>\max(3d-1,4d-3)$. In $1d$, this ingappability condition is improved to $\alpha>2$ for Type I and $\alpha>0$ for Type II by examining the energy of a state with a uniform $2\pi$ twist. Notably, in $2d$, a Type II Hamiltonian with van der Waals interaction is subject to the constraint of the theorem.

cond-mat.str-el↗

arXiv2024

Strong-to-Weak Spontaneous Symmetry Breaking in Mixed Quantum States

Symmetry in mixed quantum states can manifest in two distinct forms: strong symmetry, where each individual pure state in the quantum ensemble is symmetric with the same charge, and weak symmetry, which applies only to the entire ensemble. This paper explores a novel type of spontaneous symmetry breaking (SSB) where a strong symmetry is broken to a weak one. While the SSB of a weak symmetry is measured by the long-ranged two-point correlation function, the strong-to-weak SSB (SW-SSB) is measured by the fidelity correlator. We prove that SW-SSB is a universal property of mixed-state quantum phases, in the sense that the phenomenon of SW-SSB is robust against symmetric low-depth local quantum channels. We also show that the symmetry breaking is "spontaneous" in the sense that the effect of a local symmetry-breaking measurement cannot be recovered locally. We argue that a thermal state at a nonzero temperature in the canonical ensemble (with fixed symmetry charge) should have spontaneously broken strong symmetry. Additionally, we study non-thermal scenarios where decoherence induces SW-SSB, leading to phase transitions described by classical statistical models with bond randomness. In particular, the SW-SSB transition of a decohered Ising model can be viewed as the "ungauged" version of the celebrated toric code decodability transition. We confirm that, in the decohered Ising model, the SW-SSB transition defined by the fidelity correlator is the only physical transition in terms of channel recoverability. We also comment on other (inequivalent) definitions of SW-SSB, through correlation functions with higher Renyi indices.

quant-ph↗

arXiv2024

Symmetry Protected Topological Phases of Mixed States in the Doubled Space

The interplay of symmetry and topology in quantum many-body mixed states has recently garnered significant interest. In a phenomenon not seen in pure states, mixed states can exhibit average symmetries -- symmetries that act on component states while leaving the ensemble invariant. In this work, we systematically characterize symmetry protected topological (SPT) phases of short-range entangled (SRE) mixed states of spin systems -- protected by both average and exact symmetries -- by studying their pure Choi states in a doubled Hilbert space, where the familiar notions and tools for SRE and SPT pure states apply. This advantage of the doubled space comes with a price: extra symmetries as well as subtleties around how hermiticity and positivity of the original density matrix constrain the possible SPT invariants. Nevertheless, the doubled space perspective allows us to obtain a systematic classification of mixed-state SPT (MSPT) phases. We also investigate the robustness of MSPT invariants under symmetric finite-depth quantum channels, the bulk-boundary correspondence for MSPT phases, and the consequences of the MSPT invariants for the separability of mixed states and the symmetry-protected sign problem. In addition to MSPT phases, we study the patterns of spontaneous symmetry breaking (SSB) of mixed states, including the phenomenon of exact-to-average SSB, and the order parameters that detect them. Mixed state SSB is related to an ingappability constraint on symmetric Lindbladian dynamics.

quant-ph↗

arXiv2023

Topological Phases with Average Symmetries: the Decohered, the Disordered, and the Intrinsic

Global symmetries greatly enrich the landscape of topological quantum phases, playing an essential role from topological insulators to fractional quantum Hall effect. Topological phases in mixed quantum states, originating from \textit{decoherence} in open quantum systems or \textit{disorders} in imperfect crystalline solids, have recently garnered significant interest. Unlike pure states, mixed quantum states can exhibit \textit{average symmetries} -- symmetries that keep the total ensemble invariant but not on each individual state. In this work, we present a systematic classification and characterization of average symmetry-protected topological (ASPT) phases applicable to generic symmetry groups, encompassing both average and exact symmetries, for bosonic and fermionic systems. Moreover, we formulate the theory of average symmetry-enriched topological (ASET) orders in disordered bosonic systems. Our systematic approach helps clarify nuanced issues in previous literature and uncovers compelling new physics. Notably, we discover that (1) the definition and classification of ASPT phases in decohered and disordered systems exhibit subtle differences; (2) despite these differences, ASPT phases in both settings can be classified and characterized under a unified framework of defect decoration and spectral sequence; (3) this systematic classification uncovers a plethora of ASPT phases that are \textit{intrinsically mixed}, implying they can exclusively manifest in decohered or disordered systems where part of the symmetry is average; (4) similarly for ASET, we find intrinsically disordered phases exhibiting exotic anyon behaviors -- the ground states of such phases necessarily contain localized anyons, with gapless (yet still localized) excitation spectral.

cond-mat.str-el↗

arXiv2023

Exploring critical systems under measurements and decoherence via Keldysh field theory

We employ an $n$-replica Keldysh field theory to investigate the effects of measurements and decoherence on long distance behaviors of quantum critical states. We classify different measurements and decoherence based on their timescales and symmetry properties, and demonstrate that they can be described by $n$-replica Keldysh field theories with distinct physical and replica symmetries. Low energy effective theories for various scenarios are then derived using the symmetry and fundamental consistency conditions of the Keldysh formalism. We apply this framework to study the critical Ising model in both one and two spatial dimensions. In one dimension, we demonstrate that (1) measurements over a finite period of time along the transverse spin direction do not modify the asymptotic scaling of correlation functions and entanglement entropy, whereas (2) measurements along the longitudinal spin direction lead to an area law entangled phase. We also show that (3) decoherence noises over a finite time can be mapped to specific boundary conditions of a critical Ashkin-Teller model, and the entanglement characteristics of the resulting mixed state can be determined. For measurements and decoherence over an extensive time, we demonstrate that (4) the von Neumann entanglement entropy of a large subsystem can exhibit a (sub-)dominant logarithmic scaling in the stationary state for weak measurement (decoherence) performed in a basis that is symmetric under the Ising symmetry, but (5) reduces to an area law for measurements and decoherence in the longitudinal direction. Our results demonstrate that the Keldysh formalism is a useful tool for systematically studying the effects of measurements and decoherence on long-wavelength physics.

quant-ph↗

arXiv2022

Average Symmetry-Protected Topological Phases

Symmetry-protected topological (SPT) phases are many-body quantum states that are topologically nontrivial as long as the relevant symmetries are unbroken. In this work we show that SPT phases are also well defined for average symmetries, where quenched disorders locally break the symmetries, but restore the symmetries upon disorder averaging. An example would be crystalline SPT phases with imperfect lattices. Specifically, we define the notion of average SPT for disordered ensembles of quantum states. We then classify and characterize a large class of average SPT phases using a decorated domain wall approach, in which domain walls (and more general defects) of the average symmetries are decorated with lower dimensional topological states. We then show that if the decorated domain walls have dimension higher than $(0+1)d$, then the boundary states of such average SPT will almost certainly be long-range entangled, with probability approaching $1$ as the system size approaches infinity. This generalizes the notion of t'Hooft anomaly to average symmetries, which we dub "average anomaly". The average anomaly can also manifest as constraints on lattice systems similar to the Lieb-Schultz-Mattis (LSM) theorems, but with only average lattice symmetries. We also generalize our problem to "quantum disorders" that can admit short-range entanglement on their own, and develop a theory of such generalized average SPTs purely based on density matrices and quantum channels. Our results indicate that topological quantum phenomena associated with average symmetries can be at least as rich as those with ordinary exact symmetries.

cond-mat.str-el↗

arXiv2021

Emergent anomaly of Fermi surfaces: a simple derivation from Weyl fermions

The Fermi liquid has an emergent low-energy symmetry that corresponds to charge conservation at each momentum on the Ferm surface. Recently Else, Thorngren and Senthil (ETS) argued that the emergent symmetry had a specific t'Hooft anomaly. We give a simple derivation of the ETS anomaly using the chiral anomaly of Weyl fermions.

cond-mat.str-el↗

arXiv2021

Edge physics at the deconfined transition between a quantum spin Hall insulator and a superconductor

We study the edge physics of the deconfined quantum phase transition (DQCP) between a spontaneous quantum spin Hall (QSH) insulator and a spin-singlet superconductor (SC). Although the bulk of this transition is in the same universality class as the paradigmatic deconfined Neel to valence-bond-solid transition, the boundary physics has a richer structure due to proximity to a quantum spin Hall state. We use the parton trick to write down an effective field theory for the QSH-SC transition in the presence of a boundary. We calculate various edge properties in an $N\to\infty$ limit. We show that the boundary Luttinger liquid in the QSH state survives at the phase transition, but only as "fractional" degrees of freedom that carry charge but not spin. The physical fermion remains gapless on the edge at the critical point, with a universal jump in the fermion scaling dimension as the system approaches the transition from the QSH side. The critical point could be viewed as a gapless analogue of the quantum spin Hall state but with the full $SU(2)$ spin rotation symmetry, which cannot be realized if the bulk is gapped.

cond-mat.str-el↗

arXiv2020

Emergent QCD$_3$ Quantum Phase Transitions of Fractional Chern Insulators

Motivated by the recent work of QED$_3$-Chern-Simons quantum critical points of fractional Chern insulators (Phys. Rev. X \textbf{8}, 031015, (2018)), we study its non-Abelian generalizations, namely QCD$_3$-Chern-Simons quantum phase transitions of fractional Chern insulators. These phase transitions are described by Dirac fermions interacting with non-Abelian Chern-Simons gauge fields ($U(N)$, $SU(N)$, $USp(N)$, etc.). Utilizing the level-rank duality of Chern-Simons gauge theory and non-Abelian parton constructions, we discuss two types of QCD$_3$ quantum phase transitions. The first type happens between two Abelian states in different Jain sequences, as opposed to the QED3 transitions between Abelian states in the same Jain sequence. A good example is the transition between $\sigma^{xy}=1/3$ state and $\sigma^{xy}=-1$ state, which has $N_f=2$ Dirac fermions interacting with a $U(2)$ Chern-Simons gauge field. The second type is naturally involving non-Abelian states. For the sake of experimental feasibility, we focus on transitions of Pfaffian-like states, including the Moore-Read Pfaffian, anti-Pfaffian, particle-hole Pfaffian, etc. These quantum phase transitions could be realized in experimental systems such as fractional Chern insulators in graphene heterostructures.

cond-mat.str-el↗

arXiv2019

A theory of deconfined pseudo-criticality

It has been proposed that the deconfined criticality in $(2+1)d$ -- the quantum phase transition between a Neel anti-ferromagnet and a valence-bond-solid (VBS) -- may actually be pseudo-critical, in the sense that it is a weakly first-order transition with a generically long correlation length. The underlying field theory of the transition would be a slightly complex (non-unitary) fixed point as a result of fixed points annihilation. This proposal was motivated by existing numerical results from large scale Monte-Carlo simulations as well as conformal bootstrap. However, an actual theory of such complex fixed point, incorporating key features of the transition such as the emergent $SO(5)$ symmetry, is so far absent. Here we propose a Wess-Zumino-Witten (WZW) nonlinear sigma model with level $k=1$, defined in $2+\epsilon$ dimensions, with target space $S^{3+\epsilon}$ and global symmetry $SO(4+\epsilon)$. This gives a formal interpolation between the deconfined criticality at $d=3$ and the $SU(2)_1$ WZW theory at $d=2$ describing the spin-$1/2$ Heisenberg chain. The theory can be formally controlled, at least to leading order, in terms of the inverse of the WZW level $1/k$. We show that at leading order, there is a fixed point annihilation at $d^*\approx2.77$, with complex fixed points above this dimension including the physical $d=3$ case. The pseudo-critical properties such as correlation length, scaling dimensions and the drifts of scaling dimensions as the system size increases, calculated crudely to leading order, are qualitatively consistent with existing numerics.

cond-mat.str-el↗