arXiv subjects

Chao-Ming Jian

Publications and source records attributed to Chao-Ming Jian.

At least 19 recordsLinked to original sources

arXiv2026

Free-Fermion Measurement-Induced Volume- to Area-Law Entanglement Transition in the Presence of Fermion Interactions

At a generic volume- to area-law entanglement transition in a many-body system, quantum chaos is arrested. We argue that this tends to imply the vanishing of a certain "mass" term in the field theory of the measurement-induced phase transition (MIPT) for monitored, interacting fermions. To explore this idea, we consider the MIPT with no conserved quantities that describes 1D monitored, interacting Majorana fermions in class DIII. This is the most general problem of interacting fermions with weak fermion parity measurements. Without interactions, it is known that a noninteracting MIPT separates the area-law phase from a log-enhanced "thermal metal" phase at sufficiently weak monitoring. We conjecture that the MIPT with interactions is the same as the noninteracting one in this case; the volume-law phase arises through the dangerously irrelevant mass. The physical picture is that the mass represents a local Fermi's golden rule interparticle scattering rate density that is tantamount to the entangling rate density. The latter must vanish continuously at a continuous MIPT. On the other hand, the field theory capturing the MIPT for monitored fermions with additional continuous symmetries is expected to be different, because the interactions introduce additional terms associated to conserved Noether currents. We propose numerical tests of our conjecture. In addition, we analytically identify a candidate noninteracting critical point representing the MIPT, using a controlled $ε$-expansion.

cond-mat.stat-mech↗

arXiv2026

Trial wavefunction for fractional quantum spin Hall insulators

Fermions with opposite spins occupying half-filled conjugate Chern bands exhibit interaction physics distinct from their multi-component Landau-level counterparts with the same chirality. This is largely due to unavoidable inter-species collisions that preclude the Halperin-type wavefunctions available in multi-component Landau levels. In this work, we propose and evaluate a variational wavefunction for a fractional quantum spin Hall state with Z_4 topological order in a pair of conjugate Landau levels. This Z_4 topological order has previously been shown to be the minimal topological order compatible with charge conservation, $S_z$ conservation, time-reversal symmetry, and the fractional spin Hall conductance 1/2 suggested by previous twisted MoTe$_2$ experiments. Our construction is based on the condensation of an anyonic exciton formed by the neutral fermionic excitations in a decoupled pair of Moore-Read Pfaffian state and its conjugate. By coupling the chiral and anti-chiral Ising conformal field theories associated with the two spin species, we introduce a variational mass parameter in the Z_4 trial wavefunction that captures the inter-spin-species s-wave pairing of composite fermions alongside the intra-spin-species p-wave pairing. We assess the energetics of this trial state using Monte Carlo sampling on a spherical geometry. Because the coupled state intrinsically involves Landau-level mixing, we explicitly evaluate the resulting kinetic energy penalty. Our phase diagram reveals that the proposed Z_4 state becomes energetically favorable in a sizable region of parameter space, over both the decoupled pair of conjugate Pfaffian states and an alternative exciton condensate state. These results provide a concrete microscopic wavefunction realization of this Z_4 fractional quantum spin Hall phase, and propose a route to constructing additional families of such states.

cond-mat.str-el↗

arXiv2026

Free-Fermion Dynamics with Measurements: Topological Classification and Adaptive Preparation of Topological States

We develop a general framework for classifying fermionic dynamical systems with measurements using symmetry and topology. We introduce two complementary classification schemes based on the Altland-Zirnbauer tenfold way: (1) the many-body evolution operator (mEO) symmetry class, which classifies fermionic dynamics at the many-body level and naturally extends to interacting dynamics, and (2) the single-particle transfer matrix (sTM) symmetry class, which classifies free-fermion dynamics at the single-particle level and connects to Anderson localization physics. In the free-fermion limit, we show that these two frameworks are equivalent via a novel dynamical bulk-boundary correspondence: the topology of the dynamical system's spacetime bulk determines the topology of the area-law entangled steady-state ensemble living on its temporal boundary. Next, we prove that symmetry-invariant, post-selection-free Gaussian measurements are realizable in only four of the ten mEO classes (A, AI, BDI, D); the remaining six require either post-selection or interacting (non-Gaussian) measurements. Building on these results, we construct general post-selection-free topological adaptive circuits that realize topological dynamical phases in any spatial dimension for the four admissible mEO classes. These circuits simultaneously provide a protocol for preparing and stabilizing free-fermion topological states in all ten symmetry classes. As a concrete demonstration, we construct and simulate 2+1d adaptive circuits that realize mEO-class-A topological dynamics, steering toward a steady-state ensemble of Chern insulators in ${\cal O}(1)$ circuit depth. Finally, we numerically characterize topological phase transitions, dynamical domain-wall modes, and robustness to coherent noise, identifying finite error thresholds at which trajectory-resolved and trajectory-averaged quantities undergo distinct phase transitions.

quant-ph↗

arXiv2026

Decoding coherent errors in toric codes on honeycomb and square lattices: duality to Majorana monitored dynamics and symmetry classes

Topological stabilizer codes, such as the toric and surface codes, are leading candidates for fault-tolerant quantum computation. While their decodability under stochastic noise has been extensively studied, the effects of coherent errors, which involve quantum interference, remain less explored. In this work, we study the decodability of toric codes on honeycomb and square lattices subject to $X$- and $Z$-type coherent errors generated by the $X$- and $Z$-rotations on each qubit. We establish a duality between these decoding problems and 1+1D monitored dynamics of non-interacting Majorana fermions. This duality shows that the Altland-Zirnbauer symmetry class of the dual Majorana dynamics governs the universal structure of the decodability phase diagram. We show that the honeycomb-lattice toric code (hTC) with $X$-type error is dual to class-DIII dynamics, while the hTC with $Z$-type error and the square-lattice toric code (sTC) with both error types are dual to class-D dynamics. The key distinction arises from time-reversal symmetry. In class DIII, the generic transition out of the decodable phase is dual to a measurement-induced transition between dynamical phases with area-law and logarithmic entanglement scaling. In contrast, in class D, the generic decodability transition corresponds to a transition between two topologically distinct area-law phases. To explore these transitions in microscopic models, we consider hTC and sTC with $X$-type errors as representatives and introduce a minimal two-parameter coherent error model with spatially varying rotation angles. Using analytical and numerical methods, we map out the decodability phase diagrams and characterize the universal behavior of the transitions. We find that the decodability of sTC is more vulnerable to spatially varying coherent errors than uniform ones.

cond-mat.stat-mech↗

arXiv2025

Topological Modes in Monitored Quantum Dynamics

Dynamical quantum systems both driven by unitary evolutions and monitored through measurements have proved to be fertile ground for exploring new dynamical quantum matters. While the entanglement structure and symmetry properties of monitored systems have been intensively studied, the role of topology in monitored dynamics is much less explored. In this work, we investigate novel topological phenomena in the monitored dynamics through the lens of free-fermion systems. Free-fermion monitored dynamics were previously shown to be unified with the Anderson localization problem under the Altland-Zirnbauer symmetry classification. Guided by this unification, we identify the topological area-law-entangled phases in the former setting through the topological classification of disordered insulators and superconductors in the latter. As examples, we focus on 1+1D free-fermion monitored dynamics in two symmetry classes, DIII and A. We construct quantum circuit models to study different topological area-law phases and their domain walls in the respective symmetry classes. We find that the domain wall between topologically distinct area-law phases hosts dynamical topological modes whose entanglement is protected from being quenched by the measurements in the monitored dynamics. We demonstrate how to manipulate these topological modes by programming the domain-wall dynamics. In particular, for topological modes in class DIII, which behave as unmeasured Majorana modes, we devise a protocol to braid them and study the entanglement generated in the braiding process.

quant-ph↗

arXiv2025

Minimal Fractional Topological Insulator in half-filled conjugate moiré Chern bands

We propose a "minimal" fractional topological insulator (mFTI), motivated by the recent experimental report on the signatures of FTI at total filling factor $ν_{\rm tot} = 3$ in a transition metal dichalcogenide moiré system. The observed FTI at $ν_{\rm tot} = 3$ is likely given by a topological state living in a pair of half-filled conjugate Chern bands with Chern numbers $C=\pm 1$ on top of another pair of fully-filled conjugate Chern bands. We propose the mFTI as a strong candidate topological state in the half-filled conjugate Chern bands. The mFTI is characterized by the following features: (1) It is a fully gapped topological order (TO) with 16 Abelian anyons if the electron is considered trivial (32 including electrons); (2) the minimally-charged anyon carries electric charge $e^\ast = e/2$, together with the fractional quantum spin-Hall conductivity, implying the robustness of the mFTI's gapless edge state whenever time-reversal symmetry and charge conversation are present; (3) the mFTI is "minimal" in the sense that it has the smallest total quantum dimension (a metric for the TO's complexity) within all the TOs that can potentially be realized at the same electron filling and with the same Hall transports; the mFTI is also the unique one that respects time-reversal symmetry. (4) the mFTI is the common descendant of multiple valley-decoupled "product TOs" with larger quantum dimensions. It can also be viewed as the result of gauging multiple symmetry-protected topological states. Similar mFTIs can be constructed for a pair of $1/q$-filled conjugate Chern bands. We classify the mFTIs via the stability of the gapless interfaces between them.

cond-mat.str-el↗

arXiv2025

Field theory of monitored, interacting fermion dynamics with charge conservation

Measurement-induced phase transitions (MIPTs) in monitored quantum dynamics are non-equilibrium phase transitions between quantum-chaotic (volume-law entangled) and entanglement-suppressed, area-law phases. We reveal how monitored dynamics are situated within the framework of general far-from-equilibrium, quantum condensed-matter physics. Measurement-induced heating effects scramble the distribution function in generic (interacting) monitored fermion systems, which enables a simplified symmetry-based description of the dynamics. We demonstrate the equivalence of the Keldysh technique with the conventional Statistical-Mechanics Model for circuits, resulting from a doubled Hilbert-space (Choi-Jamiołkowski) mapping. We illustrate this using the monitored dynamics of interacting fermions with a conserved charge, deriving a unified effective field theory that captures all phases and phase transitions. The non-interacting counterpart in 1D space only has an area-law phase, with no MIPT. This was explained via an effective non-linear sigma model replica field theory possessing a very large symmetry. We show that other phases and phase transitions emerge when the replica symmetry is reduced by interactions. The reduced symmetry combines a replica permutation symmetry and charge-conservation within each replica. The former and its spontaneous breaking govern the MIPT, which can be recognized via a separatrix in the renormalization group flow. The replica-resolved charge conservation dictates the ``charge-sharpening" transition between two kinds of dynamics, where the global charge information is either hidden or reconstructible from the measurements. The field theory explains why the charge-sharpening transition should occur only in the volume-law phase. Our framework provides a template for other classes of MIPTs and situates these within the arena of non-equilibrium condensed matter physics.

cond-mat.stat-mech↗

arXiv2025

Realizing string-net condensation: Fibonacci anyon braiding for universal gates and sampling chromatic polynomials

The remarkable complexity of the vacuum state of a topologically-ordered many-body quantum system encodes the character and intricate braiding interactions of its emergent particles, the anyons.} Quintessential predictions exploiting this complexity use the Fibonacci string-net condensate (Fib-SNC) and its Fibonacci anyons to go beyond classical computing. Sampling the Fib-SNC wavefunction is expected to yield estimates of the chromatic polynomial of graph objects, a classical task that is provably hard. At the same time, exchanging anyons of Fib-SNC is expected to allow fault-tolerant universal quantum computation. Nevertheless, the physical realization of Fib-SNC and its anyons remains elusive. Here, we introduce a scalable dynamical string-net preparation (DSNP) approach, suitable even for near-term quantum processors, which dynamically prepares Fib-SNC and its anyons through reconfigurable graphs. Using a superconducting quantum processor, we couple the DSNP approach with composite error-mitigation on deep circuits to successfully create, measure, and braid anyons of Fib-SNC in a scalable manner. We certify the creation of anyons by measuring their `anyon charge', finding an average experimental accuracy of $94\%$. Furthermore, we validate that exchanging these anyons yields the { expected} golden ratio~$ϕ$ with~$98\%$ average accuracy and~$8\%$ measurement uncertainty. Finally, we sample the Fib-SNC to estimate the chromatic polynomial at~$ϕ+2$ for {several} graphs. Our results establish the proof of principle for using Fib-SNC and its anyons for fault-tolerant universal quantum computation and {for aiming at} a classically-hard problem.

quant-ph↗

arXiv2025

Average-exact mixed anomalies and compatible phases

The quantum anomaly of a global symmetry is known to strongly constrain the allowed low-energy physics in a clean and isolated quantum system. However, the effect of quantum anomalies in disordered systems is much less understood, especially when the global symmetry is only preserved on average by the disorder. In this work, we focus on disordered systems with both average and exact symmetries $A\times K$, where the exact symmetry $K$ is respected in every disorder configuration, and the average $A$ is only preserved on average by the disorder ensemble. When there is a mixed quantum anomaly between the average and exact symmetries, we argue that the mixed state representing the ensemble of disordered ground states cannot be featureless. While disordered mixed states smoothly connected to the anomaly-compatible phases in clean limit are certainly allowed, we also found disordered phases that have no clean-limit counterparts, including the glassy states with strong-to-weak symmetry breaking, and average topological orders for certain anomalies. We construct solvable lattice models to demonstrate each of these possibilities. We also provide a field-theoretic argument to provide a criterion for whether a given average-exact mixed anomaly admits a compatible average topological order.

cond-mat.str-el↗

arXiv2024

Higher-form Symmetries under Weak Measurement

We aim to address the following question: if we start with a quantum state with a spontaneously broken higher-form symmetry, what is the fate of the system under weak local quantum measurements? We demonstrate that under certain conditions, a phase transition can be driven by weak measurements, which suppresses the spontaneous breaking of the 1-form symmetry and weakens the 1-form symmetry charge fluctuation. We analyze the nature of the transitions employing the tool of duality, and we demonstrate that some of the transitions driven by weak measurement enjoy a line of fixed points with self-duality.

cond-mat.str-el↗

arXiv2024

Disorder Operator and Rényi Entanglement Entropy of Symmetric Mass Generation

In recent years a consensus has gradually been reached that the previously proposed deconfined quantum critical point (DQCP) for spin-1/2 systems, an archetypal example of quantum phase transition beyond the classic Landau's paradigm, actually does not correspond to a true unitary conformal field theory (CFT). In this work we carefully investigate another type of quantum phase transition supposedly beyond the similar classic paradigm, the so called ``symmetric mass generation" (SMG) transition proposed in recent years. We employ the sharp diagnosis including the scaling of disorder operator and Rényi entanglement entropy in large-scale lattice model quantum Monte Carlo simulations. Our results strongly suggest that the SMG transition is indeed an unconventional quantum phase transition and it should correspond to a true $(2+1)d$ unitary CFT.

cond-mat.str-el↗

arXiv2024

Tapestry of dualities in decohered quantum error correction codes

Quantum error correction (QEC) codes protect quantum information from errors due to decoherence. Many of them also serve as prototypical models for exotic topological quantum matters. Investigating the behavior of the QEC codes under decoherence sheds light on not only the codes' robustness against errors but also new out-of-equilibrium quantum phases driven by decoherence. The phase transitions, including the error threshold, of the decohered QEC codes can be probed by the systems' Rényi entropies $S_R$ with different Rényi indices $R$. In this paper, we study the general construction of the statistical models that characterize the Rényi entropies of QEC codes decohered by Pauli noise. We show that these statistical models can be organized into a "tapestry" woven by rich duality relations among them. For Calderbank-Shor-Steane (CSS) codes with bit-flip and phase-flip errors, we show that each Rényi entropy is captured by a pair of dual statistical models with randomness. For $R=2,3,\infty$, there are additional dualities that map between the two error types, relating the critical bit-flip and phase-flip error rates of the decoherence-induced phase transitions in the CSS codes. For CSS codes with an "$em$ symmetry" between the $X$-type and the $Z$-type stabilizers, the dualities with $R=2,3,\infty$ become self-dualities with super-universal self-dual error rates. These self-dualities strongly constrain the phase transitions of the code signaled by $S_{R=2,3,\infty}$. For general stabilizer codes decohered by generic Pauli noise, we also construct the statistical models that characterize the systems' entropies and obtain general duality relations between Pauli noise with different error rates.

cond-mat.str-el↗

arXiv2023

Realizing a tunable honeycomb lattice in ABBA-stacked twisted double bilayer WSe$_2$

The ideal honeycomb lattice, featuring sublattice and SU(2) spin rotation symmetries, is a fundamental model for investigating quantum matters with topology and correlations. With the rise of the moiré-based design of model systems, realizing a tunable and symmetric honeycomb lattice system with a narrow bandwidth can open access to new phases and insights. We propose the ABBA-stacked twisted double bilayer WSe$_2$ as a realistic and tunable platform for reaching this goal. Adjusting the twist angle allows the bandwidth and the ratio between hopping parameters of different ranges to be tuned. Moreover, the system's small bandwidth and spin rotation symmetry enable effective control of the electronic structure through an in-plane magnetic field. We construct an extended Hubbard model for the system to demonstrate this tunability and explore possible ordered phases using the Hartree-Fock approximation. We find that at a hole filling of $ν= 2$ (two holes per moiré unit cell), an in-plane magnetic field of a few Tesla can ``dope" the system from a semimetal to a metal. Interactions then drive an instability towards a canted antiferromagnetic insulator ground state. Additionally, we observe a competing insulating phase with sublattice charge polarization. Finally, we discuss the experimental signatures of these novel insulating phases.

cond-mat.str-el↗

arXiv2023

The Conjugate Composite Fermi Liquid

Recent experimental observations of the fractional quantum anomalous Hall effect in spin/valley polarized moiré systems call for a more expansive theoretical exploration of strongly correlated physics in partially filled topological bands. In this work we study a state that we refer to as the conjugate-composite Fermi liquid (cCFL), which arises when a pair of Chern bands with opposite Chern numbers are both half-filled. We demonstrate that the cCFL is the parent state of various interesting phenomena. As an example, we demonstrate that with the existence of an inplane spin order, the cCFL could be driven into a quantum bad metal phase, in the sense that it is a metallic phase whose zero temperature longitudinal resistivity is finite, but far greater than the Mott-Ioffe-Regal limit, i.e. $ρ^e_{xx} \gg h/e^2$. The bad metal phase is also accompanied with a new Wiedemann-Franz law, meaning the thermal conductivity is proportional to the electrical resistivity rather than conductivity. Other proximate phases of the cCFL such as superconductivity and a chiral spin liquid phase can occur when the composite fermions (CF) form the inter-valley CF-exciton condensate.

cond-mat.str-el↗

arXiv2023

Intertwined fractional quantum anomalous Hall states and charge density waves

Motivated by the recent experimental breakthrough on the observation of the fractional quantum anomalous Hall (FQAH) effects in semiconductor and graphene moiré materials, we explore the rich physics associated with the coexistence of FQAH effect and the charge density wave (CDW) order that spontaneously breaks the translation symmetry. We refer to a state with both properties as "FQAH-crystal". We show that the interplay between FQAH effect and CDW can lead to a rich phase diagram including multiple topological phases and topological quantum phase transitions at the same moiré filling. In particular, we demonstrate the possibility of direct quantum phase transitions from a FQAH-crystal with Hall conductivity $σ_H = - 2/3$ to a trivial CDW insulator with $σ_H = 0$, and more interestingly, to a QAH-crystal with $σ_H= -1$.

cond-mat.str-el↗

arXiv2023

Entanglement in one-dimensional critical state after measurements

The entanglement entropy (EE) of the ground state of a one-dimensional Hamiltonian at criticality has a universal logarithmic scaling with a prefactor given by the central charge $c$ of the underlying 1+1d conformal field theory. When the system is probed by measurements, the entanglement in the critical ground state is inevitably affected due to wavefunction collapse. In this paper, we study the effect of weak measurements on the entanglement scaling in the ground state of the one-dimensional critical transverse-field Ising model. For the measurements of the spins along their transverse spin axis, we identify interesting post-measurement states associated with spatially uniform measurement outcomes. The EE in these states still satisfies the logarithmic scaling but with an alternative prefactor given by the effective central charge $c_{\text{eff}}$. We derive the analytical expression of $c_{\text{eff}}$ as a function of the measurement strength. Using numerical simulations, we show that for the EE averaged over all post-measurement states based on their Born-rule probabilities, the numerically extracted effective central charge appears to be independent of the measurement strength, contrary to the usual expectation that local and non-overlapping measurements reduce the entanglement in the system. We also examine the behavior of the average EE under (biased) forced measurements where the measurement outcomes are sampled with a pre-determined probability distribution without inter-site correlations. In particular, we find an optimal probability distribution that can serve as a mean-field approximation to the Born-rule probabilities and lead to the same $c_{\text{eff}}$ behavior. The effects of the measurements along the longitudinal spin axis and the post-measurement correlation functions are also discussed.

quant-ph↗

arXiv2023

Subsystem symmetry, spin glass order, and criticality from random measurements in a two-dimensional Bacon-Shor circuit

We study a 2D measurement-only random circuit motivated by the Bacon-Shor error correcting code. We find a rich phase diagram as one varies the relative probabilities of measuring nearest neighbor Pauli XX and ZZ check operators. In the Bacon-Shor code, these checks commute with a group of stabilizer and logical operators, which therefore represent conserved quantities. Described as a subsystem symmetry, these conservation laws lead to a continuous phase transition between an X-basis and Z-basis spin glass order. The two phases are separated by a critical point where the entanglement entropy between two halves of an L X L system scales as L ln L, a logarithmic violation of the area law. We generalize to a model where the check operators break the subsystem symmetries (and the Bacon-Shor code structure). In tension with established heuristics, we find that the phase transition is replaced by a smooth crossover, and the X- and Z-basis spin glass orders spatially coexist. Additionally, if we approach the line of subsystem symmetries away from the critical point in the phase diagram, some spin glass order parameters jump discontinuously

quant-ph↗

arXiv2023

Quantum criticality under decoherence or weak measurement

Decoherence inevitably happens when a quantum state is exposed to its environment, which can affect quantum critical points (QCP) in a nontrivial way. As was pointed out in recent literature on $(1+1)d$ conformal field theory (CFT), the effect of weak measurement can be mathematically mapped to the problem of boundary CFT. In this work, we focus on the $(2+1)d$ QCPs, whose boundary and defect effects have attracted enormous theoretical and numerical interests very recently. We focus on decoherence caused by weak measurements with and without post-selecting the measurement outcomes. Our main results are: (1) for an O(N) Wilson-Fisher QCP under weak measurement with post-selection, an observer would in general observe two different types of boundary/defect criticality with very different behaviors from the well-known Wilson-Fisher fixed points; in particular, it is possible to observe the recently proposed exotic "extraordinary-log" correlation. (2) An extra quantum phase transition can be driven by decoherence, if we consider quantities nonlinear with the decohered density matrix, such as the Renyi entropy. We demonstrate the connection between this transition to the information-theoretic transition driven by an error in the toric code model. (3) When there is no post-selection, though correlation functions between local operators remain the same as the undecohered pure state, nonlocal operators such as the "disorder operator" would have qualitatively distinct behaviors; and we also show that the decoherence can lead to confinement.

cond-mat.stat-mech↗