arXiv subjects

Yohei Fuji

Publications and source records attributed to Yohei Fuji.

At least 19 recordsLinked to original sources

arXiv2026

Effective Hamiltonian description on monitored Majorana chains: correlated power-law hoppings and unconventional entanglement scaling

We investigate the structures of effective Hamiltonians governing monitored dynamics of a one-dimensional Majorana chain through the Lyapunov spectral analysis. We focus on a gapless phase characterized by finite-size scalings different from those in conventional critical and/or frustration-free systems; the spectral gap closing faster than $1/L$ but slower than $1/L^2$ and the entanglement entropy growing as $[\ln(L)]^2$ with $L$ being the system size. We find that the corresponding effective Hamiltonians have random long-range power-law hoppings with nontrivial magnitude correlations, rather than being independently and identically distributed. To elucidate the role of these non-Gaussian correlations, we construct random power-law hopping models that capture the essential features of the effective Hamiltonians. The spectral gaps of the constructed models decay faster than $1/L$ but slower than $1/L^2$. We find that, in the absence of hopping correlations, the ground-state entanglement exhibits $\ln(L)$ scaling. In the presence of correlations, by contrast, the entanglement entropy is enhanced and its system-size dependence is consistent with $[\ln(L)]^2$ scaling over the system sizes studied. These results suggest that correlations among long-range hopping magnitudes are responsible for the entanglement scaling that seldom appears in ground states of conventional isolated quantum systems.

cond-mat.stat-mech↗

arXiv2026

Phase transitions in coupled Ising chains and SO($N$)-symmetric spin chains

We investigate the nature of quantum phase transitions in a (1+1)-dimensional field theory composed of $N$ copies of the Ising conformal field theory interacting via competing relevant perturbations. The field theory governs the competition between a mass term and an interaction involving the product of $N$ order-parameter fields, which is realized, e.g. in coupled Ising chains, two-leg spin ladders, and SO($N$)-symmetric spin chains. By combining a perturbative renormalization group analysis and large-scale matrix-product state simulations, we systematically determine the nature of the phase transition as a function of $N$. For $N=2$ and $N=3$, we confirm that the transition is continuous, belonging to the Ising and four-state Potts universality classes, respectively. In contrast, for $N \ge 4$, our results provide compelling evidence that the transition becomes first order. We further apply these findings to specific lattice models with SO($N$) symmetry, including spin-$1/2$ and spin-$1$ two-leg ladders, that realize a direct transition between an SO($N$) symmetry-protected topological phase and a trivial phase. Our results refine a recent conjecture regarding the criticality of transitions between SPT phases.

cond-mat.str-el↗

arXiv2025

An introduction to monitored quantum systems and quantum trajectories: spectrum, typicality, and phases

Thanks to recent experimental advances in simulating and detecting quantum dynamics with high precision and controllability, our understanding of the physics of monitored quantum systems has considerably deepened over the past decades. In this article, we provide an introductory theoretical review on the basic formalisms governing open quantum dynamics under measurement, along with recent developments in their spectral and typical aspects. After reviewing quantum measurement theory, we introduce the concept of quantum trajectories, which are the conditional dynamics of monitored states shaped by a set of measurement outcomes. We then discuss the spectral properties of the dynamical map describing the evolution averaged over measurement outcomes. As has recently been recognized, these spectral features are intimately connected to whether quantum trajectories exhibit typical behaviors, such as ergodicity and purification. Moreover, we introduce Lyapunov exponents of typical quantum trajectories and discuss how these quantities serve as indicators of measurement-induced phase transitions in monitored quantum many-body systems.

cond-mat.stat-mech↗

arXiv2024

Topology and Spectrum in Measurement-Induced Phase Transitions

Competition among repetitive measurements of noncommuting observables and unitary dynamics can give rise to a wide variety of entanglement phases. Here, we propose a general framework based on Lyapunov analysis to characterize topological properties in monitored quantum systems through their spectrum and many-body topological invariants. We illustrate this framework by analyzing (1+1)-dimensional monitored circuits for Majorana fermions, which are known to exhibit topological and trivial area-law entangled phases as well as a critical phase with sub-volume-law entanglement. Through the Lyapunov analysis, we identify the presence (absence) of edge-localized zero modes inside the bulk gap in the topological (trivial) phase and a bulk gapless spectrum in the critical phase. Furthermore, by suitably exploiting the fermion parity with twisted measurement outcomes at the boundary, we construct a topological invariant that distinguishes the two area-law phases and dynamically characterizes the critical phase. Our framework thus provides a general route to extend the notion of bulk-edge correspondence to monitored quantum dynamics.

quant-ph↗

arXiv2024

Multifractality in monitored single-particle dynamics

We study multifractal properties in time evolution of a single particle subject to repeated measurements. For quantum systems, we consider circuit models consisting of local unitary gates and local projective measurements. For classical systems, we consider models for estimating the trajectory of a particle evolved under local transition processes by partially measuring particle occupations. In both cases, multifractal behaviors appear in the ensemble of wave functions or probability distributions conditioned on measurement outcomes after a sufficiently long time. While the nature of particle transport (diffusive or ballistic) qualitatively affects the multifractal properties, they are even quantitatively robust to the measurement rate or specific protocols. On the other hand, multifractality is generically lost by generalized measurements allowing erroneous outcomes or by postselection of the outcomes with no particle detection. We demonstrate these properties by numerical simulations and also propose several simplified models, which allow us to analytically obtain multifractal properties in the monitored single-particle systems.

quant-ph↗

arXiv2024

Floquet Flux Attachment in Cold Atomic Systems

Flux attachment provides a powerful conceptual framework for understanding certain forms of topological order, including most notably the fractional quantum Hall effect. Despite its ubiquitous use as a theoretical tool, directly realizing flux attachment in a microscopic setting remains an open challenge. Here, we propose a simple approach to realizing flux attachment in a periodically-driven (Floquet) system of either spins or hard-core bosons. We demonstrate that such a system naturally realizes correlated hopping interactions and provides a sharp connection between such interactions and flux attachment. Starting with a simple, nearest-neighbor, free boson model, we find evidence -- from both a coupled wire analysis and large-scale density matrix renormalization group simulations -- that Floquet flux attachment stabilizes the bosonic integer quantum Hall state at $1/4$ filling (on a square lattice), and the Halperin-221 fractional quantum Hall state at $1/6$ filling (on a honeycomb lattice). At $1/2$ filling on the square lattice, time-reversal symmetry is instead spontaneously broken and bosonic integer quantum Hall states with opposite Hall conductances are degenerate. Finally, we propose an optical-lattice-based implementation of our model on a square lattice and discuss prospects for adiabatic preparation as well as effects of Floquet heating.

quant-ph↗

arXiv2022

Ground state degeneracy on torus in a family of $\mathbb{Z}_N$ toric code

Topologically ordered phases in $2+1$ dimensions are generally characterized by three mutually-related features: fractionalized (anyonic) excitations, topological entanglement entropy, and robust ground state degeneracy that does not require symmetry protection or spontaneous symmetry breaking. Such degeneracy is known as topological degeneracy and usually can be seen under the periodic boundary condition regardless of the choice of the system size $L_1$ and $L_2$ in each direction. In this work we introduce a family of extensions of the Kitaev toric code to $N$ level spins ($N\geq2$). The model realizes topologically ordered phases or symmetry-protected topological phases depending on parameters in the model. The most remarkable feature of the topologically ordered phases is that the ground state may be unique, depending on $L_1$ and $L_2$, despite that the translation symmetry of the model remains unbroken. Nonetheless, the topological entanglement entropy takes the nontrivial value. We argue that this behavior originates from the nontrivial action of translations permuting anyon species.

cond-mat.other↗

arXiv2022

Charge fluctuation and charge-resolved entanglement in a monitored quantum circuit with $U(1)$ symmetry

We study a (1+1)-dimensional quantum circuit consisting of Haar-random unitary gates and projective measurements that conserve a total $U(1)$ charge and thus have $U(1)$ symmetry. In addition to a measurement-induced entanglement transition between a volume-law and an area-law entangled phase, we find a phase transition between two phases characterized by bipartite charge fluctuation growing with the subsystem size or staying constant. At this charge-fluctuation transition, steady-state quantities obtained by evolving an initial state with a definitive total charge exhibit critical scaling behaviors akin to Tomonaga-Luttinger-liquid theory for equilibrium critical quantum systems with $U(1)$ symmetry, such as logarithmic scaling of bipartite charge fluctuation, power-law decay of charge correlation functions, and logarithmic scaling of charge-resolved entanglement whose coefficient becomes a universal quadratic function in a flux parameter. These critical features, however, do not persist below the transition in contrast to a recent prediction based on replica field theory and mapping to a classical statistical mechanical model.

cond-mat.dis-nn↗

arXiv2021

Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders

Three-dimensional (3D) gapped topological phases with fractional excitations are divided into two subclasses: one has topological order with point-like and loop-like excitations fully mobile in the 3D space, and the other has fracton order with point-like excitations constrained in lower-dimensional subspaces. These exotic phases are often studied by exactly solvable Hamiltonians made of commuting projectors, which, however, are not capable of describing those exhibiting surface states with gapless chiral dispersion. Here we introduce a systematic way, based on cellular construction recently proposed for 3D topological phases, to construct another type of exactly solvable models in terms of coupled quantum wires with given inputs of cellular structure, two-dimensional Abelian topological order, and their gapped interfaces. We show that our models can describe both 3D topological and fracton orders (and even their hybrid) and study their universal properties such as quasiparticle statistics and topological ground-state degeneracy. We also apply this construction to two-dimensional coupled-wire models with ordinary topological orders and translation-symmetry-enriched topological orders. Our results pave the way for effective quantum field theory descriptions or microscopic model realizations of fracton orders with chiral gapless surface states.

cond-mat.str-el↗

arXiv2021

Bloch oscillations in the spin-1/2 XXZ chain

Under a perfect periodic potential, the electric current density induced by a constant electric field may exhibit nontrivial oscillations, so-called Bloch oscillations, with an amplitude that remains nonzero in the large system size limit. Such oscillations have been well studied for nearly noninteracting particles and observed in experiments. In this work, we revisit Bloch oscillations in strongly interacting systems. By analyzing the spin-1/2 XXZ chain, which can be mapped to a model of spinless electrons, we demonstrate that the current density at special values of the anisotropy parameter $\Delta=-\cos(\pi/p)$ ($p=3,4,5,\cdots$) in the ferromagnetic gapless regime behaves qualitatively the same as in the noninteracting case ($\Delta=0$) even in the weak electric field limit. When $\Delta$ deviates from these values, the amplitude of the oscillation under a weak electric field is suppressed by a factor of the system size. We estimate the strength of the electric field required to observe such a behavior using the Landau--Zener formula.

cond-mat.str-el↗

arXiv2020

Measurement-induced quantum criticality under continuous monitoring

We investigate entanglement phase transitions from volume-law to area-law entanglement in a quantum many-body state under continuous position measurement on the basis of the quantum trajectory approach. We find the signatures of the transitions as peak structures in the mutual information as a function of measurement strength, as previously reported for random unitary circuits with projective measurements. At the transition points, the entanglement entropy scales logarithmically and various physical quantities scale algebraically, implying emergent conformal criticality, for both integrable and nonintegrable one-dimensional interacting Hamiltonians; however, such transitions have been argued to be absent in noninteracting regimes in some previous studies. With the aid of $U(1)$ symmetry in our model, the measurement-induced criticality exhibits a spectral signature resembling a Tomonaga-Luttinger liquid theory from symmetry-resolved entanglement. These intriguing critical phenomena are unique to steady-state regimes of the conditional dynamics at the single-trajectory level, and are absent in the unconditional dynamics obeying the Lindblad master equation, in which the system ends up with the featureless, infinite-temperature mixed state. We also propose a possible experimental setup to test the predicted entanglement transition based on the subsystem particle-number fluctuations. This quantity should readily be measured by the current techniques of quantum gas microscopy and is in practice easier to obtain than the entanglement entropy itself.

cond-mat.stat-mech↗

arXiv2019

Anisotropic layer construction of anisotropic fracton models

We propose a coupled-layer construction of a class of fracton topological orders in three spatial dimensions, which is characterized by spatially anisotropic mobility of quasiparticle excitations constrained in subdimensional manifolds. The simplest model is obtained by stacking and coupling layers of the two-dimensional toric codes on the square lattice and can be exactly solved in the strong-coupling limit. The resulting fracton excitations are understood as a consequence of anyon pair condensation induced by the coupling between layers. We also present generalizations of the construction for layers of the Kitaev-honeycomb models, the $Z_N$ toric codes, and the toric codes and the doubled semion models on the honeycomb lattice.

cond-mat.str-el↗

arXiv2019

From coupled wires to coupled layers: Model with three-dimensional fractional excitations

We propose a systematic approach to constructing microscopic models with fractional excitations in three-dimensional (3D) space. Building blocks are quantum wires described by the (1+1)-dimensional conformal field theory (CFT) associated with a current algebra $\mathfrak{g}$. The wires are coupled with each other to form a 3D network through the current-current interactions of $\mathfrak{g}_1$ and $\mathfrak{g}_2$ CFTs that are related to the $\mathfrak{g}$ CFT by a nontrivial conformal embedding $\mathfrak{g} \supset \mathfrak{g}_1 \times \mathfrak{g}_2$. The resulting model can be viewed as a layer construction of a 3D topologically ordered state, in which the conformal embedding in each wire implements the anyon condensation between adjacent layers. Local operators acting on the ground state create point-like or loop-like deconfined excitations depending on the branching rule. We demonstrate our construction for a simple solvable model based on the conformal embedding $SU(2)_1 \times SU(2)_1 \supset U(1)_4 \times U(1)_4$. We show that the model possesses extensively degenerate ground states on a torus with deconfined quasiparticles, and that appropriate local perturbations lift the degeneracy and yield a 3D $Z_2$ gauge theory with a fermionic $Z_2$ charge.

cond-mat.str-el↗

arXiv2018

Quantum Hall hierarchy from coupled wires

The coupled-wire construction provides a useful way to obtain microscopic Hamiltonians for various two-dimensional topological phases, among which fractional quantum Hall states are paradigmatic examples. Using the recently introduced flux attachment and vortex duality transformations for coupled wires, we show that this construction is remarkably versatile to encapsulate phenomenologies of hierarchical quantum Hall states: the Jain-type hierarchy states of composite fermions filling Landau levels and the Haldane-Halperin hierarchy states of quasiparticle condensation. The particle-hole conjugate transformation for coupled-wire models is also given as a special case of the hierarchy construction. We also propose coupled-wire models for the composite Fermi liquid, which turn out to be compatible with a sort of the particle-hole symmetry implemented in a nonlocal way at $\nu=1/2$. Furthermore, our approach shows explicitly the connection between the Moore-Read Pfaffian state and a chiral $p$-wave pairing of the composite fermions. This composite fermion picture is also generalized to a family of the Pfaffian state, including the anti-Pfaffian state and Bonderson-Slingerland hierarchy states.

cond-mat.str-el↗

arXiv2016

Bridging coupled wires and lattice Hamiltonian for two-component bosonic quantum Hall states

We investigate a model of hard-core bosons with correlated hopping on the honeycomb lattice in an external magnetic field by means of a coupled-wire approach. It has been numerically shown that this model exhibits at half filling the bosonic integer quantum Hall (BIQH) state, which is a symmetry-protected topological phase protected by the $U(1)$ particle conservation [Y.-C. He et al., Phys. Rev. Lett. 115, 116803 (2015)]. By combining the bosonization approach and a coupled-wire construction, we analytically confirm this finding and show that it even holds in the strongly anisotropic (quasi-one-dimensional) limit. We discuss the stability of the BIQH phase against tunneling that break the separate particle conservations on different sublattices down to a global particle conservation. We further argue that a phase transition between two different BIQH phases is in a deconfined quantum critical point described by two copies of the (2+1)-dimensional $O(4)$ nonlinear sigma model with the topological $\theta$ term at $\theta=\pi$. Finally we predict a possible fractional quantum Hall state, the Halperin (221) state, at 1/6 filling.

cond-mat.str-el↗

arXiv2015

Kagome spin liquid: a deconfined critical phase driven by $U(1)$ gauge fluctuation

We investigate the nature of quantum spin liquid (QSL) phase of the spin-$1/2$ nearest-neighbor XXZ antiferromagnet on the kagome lattice. Recent numerical calculations suggest that such a kagome spin liquid is insensitive to the XXZ anisotropy and is adjacent to a chiral spin liquid phase. Reformulating the problem in terms of a $U(1)$ lattice gauge theory with dynamical bosonic spinons, we propose that the kagome spin liquid can be understood as a deconfined critical phase extended by the $U(1)$ gauge fluctuation from a deconfined critical point between a symmetry-protected topological phase and a superfluid phase. Crucially, the stability of this QSL is ensured by the gauge fluctuation and hence our description necessarily falls beyond the conventional mean-field constructions of QSLs. Our work also makes an interesting connection between the critical spin liquid, deconfined criticality, symmetry protected topological phase and topological order.

cond-mat.str-el↗

arXiv2014

Effective field theory for one-dimensional valence-bond-solid phases and their symmetry protection

We investigate valence-bond-solid (VBS) phases in one-dimensional spin systems by an effective field theory developed by Schulz [Phys. Rev. B 34, 6372 (1986)]. While the distinction among the VBS phases are often understood in terms of different entanglement structures protected by certain symmetries, we adopt a different but more fundamental point of view, that is, different VBS phases are separated by a gap closing under certain symmetries. In this way, the effective field theory reproduces the known three symmetries: time reversal, bond-centered inversion, and dihedral group of spin rotations. It also predicts that there exists another symmetry: site-centered inversion combined with a spin rotation by $\pi$. We demonstrate that the last symmetry gives distinct trivial phases, which cannot be characterized by their entanglement structure, in terms of a simple perturbative analysis in a spin chain. We also discuss several applications of the effective field theory to the phase transitions among VBS phases in microscopic models and an extension of the Lieb-Schultz-Mattis theorem to non-translational-invariant systems.

cond-mat.str-el↗

arXiv2014

Distinct trivial phases protected by a point-group symmetry in quantum spin chains

The ground state of the $S=1$ antiferromagnetic Heisenberg chain belongs to the Haldane phase -- a well known example of symmetry-protected topological phase. A staggered field applied to the $S=1$ antiferromagnetic chain breaks all the symmetries that protect the Haldane phase as a topological phase, reducing it to a trivial phase. That is, the Haldane phase is then connected adiabatically to an antiferromagnetic product state. Nevertheless, as long as the symmetry under site-centered inversion combined with a spin rotation is preserved, the phase is still distinct from another trivial phase. We demonstrate the existence of such distinct symmetry-protected trivial phases using a field-theoretical approach and numerical calculations. Furthermore, a general proof and a non-local order parameter are given in terms of an matrix-product state formulation.

cond-mat.str-el↗