arXiv subjects

Byungmin Kang

Publications and source records attributed to Byungmin Kang.

18 recordsLinked to original sources

arXiv2026

Scalable Quantum Algorithms for Gutzwiller Projection

Quantum simulation requires highly accurate input states. Gutzwiller-projected Bardeen-Cooper-Schrieffer (BCS) states provide physically motivated input states for solving strongly correlated lattice models, but their preparation on a quantum computer is hindered by the non-trivial nature of the Gutzwiller projection. We construct scalable quantum algorithms for this task by combining a circuit construction for arbitrary BCS states with the amplitude amplification for Gutzwiller projection (AAGP) procedure. AAGP yields a quadratic reduction in the number of projection queries compared with measurement-based postselection and leads to substantially improved fault-tolerant resource scaling. For projected BCS states optimized for the square-lattice $t$-$J$ model, we find that the projected-state weight decreases exponentially with system size, but the quadratic improvement is still large enough at physically relevant finite sizes to make a decisive practical difference. In particular, for a 100-site benchmark, AAGP reduces the required number of projection queries by about seven orders of magnitude. These results establish AAGP as an enabling input-state preparation protocol for projected BCS states in quantum simulation.

quant-ph↗

arXiv2026

Dirac node pinning from Dzyaloshinskii-Moriya interactions in a Kagome spin liquid

Recent experiments on the Kagome spin liquid candidate YCOB suggest the presence of Dirac fermionic spinons near the magnetization plateau at 1/9. Theories suggest that the spinons are charge neutral spin-$1/2$ excitations, in a $2π/3$ flux which triples the unit cell. Generally a gap is expected, and there is no symmetry protection for the Dirac nodes in this system. The question arises as to what causes the nodes and stabilizes them. In this work, we propose a node-creation and node-pinning mechanism driven by the Dzyaloshinskii-Moriya (DM) interactions. Employing Gutzwiller-projected variational Monte Carlo calculations, we demonstrate that DM interactions induce a band closing phase transition in the spinon spectrum. There is a change in the Chern number when the bands are inverted. Together with the DM-generated internal gauge flux, the coupling to the spinon orbital magnetization counteracts the band reopening. This interplay energetically pins the Dirac nodes over a range of parameters, resulting in a pinning mechanism distinct from the usual one from symmetry protection.

cond-mat.str-el↗

arXiv2025

Multi-Particle Quantum Walks in a Dipole-Conserving Bose-Hubbard Model

When particles move through a crystal or optical lattice, their motion can sometimes become frozen by strong external forces -- yet collective motion may still emerge through subtle many-body effects. In this work, we explore such constrained dynamics by realizing a dipole-conserving Bose-Hubbard model, where single atoms are immobile but pairs of particles can move cooperatively while preserving the system's center of mass, i.e. the overall dipole moment of the particle distribution. Starting from a one-dimensional chain of ultracold bosonic atoms in an optical lattice, we generate localized dipole excitations consisting of a hole and a doublon using site-resolved optical potentials and characterize their quantum walks and scattering dynamics. Our study provides a bottom-up investigation of a Hamiltonian with kinetic constraints, and paves the way for exploring low-energy phases of fractonic matter in existing experimental platforms.

cond-mat.quant-gas↗

arXiv2025

Cyclotron reonance in a kagome spin liquid candidate material

We propose cyclotron resonance as an optical probe for emergent fractionalized excitations in $\mathrm{U}(1)$ quantum spin liquids, focusing on kagome antiferromagnets. In contrast to conventional systems, where cyclotron resonance directly couples to charged carriers, spinons in spin liquids are charge-neutral and interact only through an emergent gauge field. We identify two key mechanisms by which an external physical electromagnetic field induces emergent electric and magnetic fields, enabling indirect coupling to spinons. Using these mechanisms, we compute the absorption rate of the cyclotron resonance response for Dirac spinons forming Landau levels. Our analysis shows that, although the absorption per layer is small, the absence of a skin-depth limitation in insulating spin liquids allows for cumulative absorption comparable to graphene in realistic sample sizes for the recently discovered spin-liquid candidate material YCu${}_3$(OH)${}_6$Br${}_2$[Br${}_{1-y}$(OH)${}_y$]. Our findings shows that cyclotron resonance is a viable experimental probe of spinon Landau quantization and emergent gauge fields, providing powerful positive experimental signatures of quantum spin liquids.

cond-mat.str-el↗

arXiv2025

2D Quon Language: Unifying Framework for Cliffords, Matchgates, and Beyond

Simulating generic quantum states and dynamics is practically intractable using classical computers. However, certain special classes -- namely Clifford and matchgate circuits -- permit efficient computation. They provide invaluable tools for studying many-body physics, quantum chemistry, and quantum computation. While both play foundational roles across multiple disciplines, the origins of their tractability seem disparate, and their relationship remain unclear. A deeper understanding of such tractable classes could expand their scope and enable a wide range of new applications. In this work, we make progress toward the unified understanding of the Clifford and matchgate -- these two classes are, in fact, distinct special cases of a single underlying structure. Specifically, we introduce the 2D Quon language, which combines Majorana worldlines with their underlying spacetime topology to diagrammatically represent quantum processes and tensor networks. In full generality, the 2D Quon language is universal -- capable of representing arbitrary quantum states, dynamics, or tensor networks -- yet they become especially powerful in describing Clifford and matchgate classes. Each class can be efficiently characterized in a visually recognizable manner using the Quon framework. This capability naturally gives rise to several families of efficiently computable tensor networks introduced in this work: punctured matchgates, hybrid Clifford-matchgate-MPS, and ansatze generated from factories of tractable networks. All of these exhibit high non-Cliffordness, high non-matchgateness, and large bipartite entanglement entropy. We discuss a range of applications of our approach, from recovering well-known results such as the Kramers-Wannier duality and the star-triangle relation of the Ising model, to enabling variational optimization with novel ansatz states.

quant-ph↗

arXiv2024

Unconventional Magnetic Oscillations in Kagome Mott Insulators

In metals, electrons in a magnetic field undergo cyclotron motion, leading to oscillations in physical properties called quantum oscillations. This phenomenon has never been seen in a robust insulator because there are no mobile electrons. We report the first exception to this rule. We study a Mott insulator on a kagome lattice which does not order magnetically down to milli-Kelvin temperatures despite antiferromagnetic interactions. We observe a plateau at magnetization equal to 1/9 Bohr magneton per magnetic ion, accompanied by oscillations in the magnetic torque, reminiscent of quantum oscillations in metals. The temperature dependence obeys Fermi distribution. These phenomena are consistent with a quantum spin liquid state whose excitations are fermionic spinons with a Dirac-like spectrum coupled to an emergent gauge field.

cond-mat.str-el↗

arXiv2024

Thermodynamic evidence of fermionic behavior in the vicinity of one-ninth plateau in a kagome antiferromagnet

The spin-1/2 kagome Heisenberg antiferromagnets are believed to host exotic quantum entangled states. Recently, the report of 1/9 magnetization plateau and magnetic oscillations in a kagome antiferromagnet YCu$_3$(OH)$_6$Br$_2$[Br$_x$(OH)$_{1-x}$] (YCOB) have made this material a promising candidate for experimentally realizing quantum spin liquid states. Here we present measurements of the specific heat $C_p$ in YCOB in high magnetic fields (up to 41.5 Tesla) down to 0.46 Kelvin, and the 1/9 plateau feature has been confirmed. Moreover, the temperature dependence of $C_p/T$ in the vicinity of 1/9 plateau region can be fitted by a linear in $T$ term which indicates the presence of a Dirac spectrum, together with a constant term, which indicates a finite density of states (DOS) contributed by other Fermi surfaces. Surprisingly the constant term is highly anisotropic in the direction of the magnetic field. Additionally, we observe a double-peak feature near $30$~T above the 1/9 plateau which is another hallmark of fermionic excitations in the specific heat.

cond-mat.str-el↗

arXiv2024

Generation of gauge magnetic fields in a kagome spin liqud candidate using the Dzyaloshinskii-Moriya interaction

The recent discovery of magnetization oscillations in a kagome spin liquid candidate motivates us to examine the origin of the gauge magnetic field term that can give rise to quantum oscillations of fermionic spinons. We find that in the presence of the Dzyaloshinskii-Moriya interaction and an average spin polarization, the spin permutation operator around the unit cell acquires an imaginary part, and a net gauge flux is generated through the unit cell of the kagome lattice. This new mechanism of gauge field generation can account for the strength of the gauge magnetic field needed to explain the experiment.

cond-mat.str-el↗

arXiv2022

Robust Interlayer-Coherent Quantum Hall States in Twisted Bilayer Graphene

We introduce a novel two-dimensional electronic system with ultrastrong interlayer interactions, namely twisted bilayer graphene with a large twist angle, as an ideal ground for realizing interlayer-coherent excitonic condensates. In these systems, subnanometer atomic separation between the layers allows significant interlayer interactions, while interlayer electron tunneling is geometrically suppressed due to the large twist angle. By fully exploiting these two features we demonstrate that a sequence of odd-integer quantum Hall states with interlayer coherence appears at the second Landau level (N = 1). Notably the energy gaps for these states are of order 1 K, which is several orders of magnitude greater than those in GaAs. Furthermore, a variety of quantum Hall phase transitions are observed experimentally. All the experimental observations are largely consistent with our phenomenological model calculations. Hence, we establish that a large twist angle system is an excellent platform for high-temperature excitonic condensation.

cond-mat.mes-hall↗

arXiv2022

Metrology of Band Topology via Resonant Inelastic X-ray Scattering

Topology is a central notion in the classification of band insulators and characterization of entangled many-body quantum states. In some cases, it manifests as quantized observables such as quantum Hall conductance. However, being inherently a global property depending on the entirety of the system, its direct measurement has remained elusive to local experimental probes in many cases. Here, we demonstrate that various topological band indices can be directly probed by resonant inelastic x-ray scattering. Specifically, we show that the crystalline symmetry eigenvalues at the high-symmetry momentum points, which determine the band topology, leads to distinct scattering intensity for particular momentum and energy. Our approach can be explicitly demonstrated in several examples such as 1D Su-Schrieffer-Heeger chain, 2D quadrupole insulator, 3D topological band insulator, and chiral hinge insulator. Our result establishes an incisive bulk probe for the measurement of band topology.

cond-mat.str-el↗

arXiv2021

Many-Body Quadrupolar Sum Rule for Higher-Order Topological Insulator

The modern theory of polarization establishes the bulk-boundary correspondence for the bulk polarization. In this paper, we attempt to extend it to a sum rule of the bulk quadrupole moment by employing a many-body operator introduced in [Phys. Rev. B 100, 245134 (2019)] and [Phys. Rev. B 100, 245135 (2019)]. The sum rule that we propose consists of the alternating sum of four observables, which are the phase factors of the many-body operator in different boundary conditions. We demonstrate its validity through extensive numerical computations for various non-interacting tight-binding models. We also observe that individual terms in the sum rule correspond to the bulk quadrupole moment, the edge-localized polarizations, and the corner charge in the thermodynamic limit on some models.

cond-mat.str-el↗

arXiv2021

Sign-Problem-Free Variant of Complex Sachdev-Ye-Kitaev Model

We construct a sign-problem free variant of the complex Sachdev-Ye-Kitaev (SYK) model which keeps all the essential properties of the SYK model, including the analytic solvability in the large-$N$ limit and being maximally chaotic. In addition to the number of complex fermions $N$, our model has an additional parameter $M$ controlling the number of terms in the Hamiltonian which we take $M \to \infty$ with keeping $M/N$ constant in the large-$N$ limit. While our model respects global $U(1)$ symmetry associated with the fermion number conservation, both the large-$N$ limit and the sign-problem free nature become explicit in the Majorana representation. We present a detailed analysis on our model, i.e., the random matrix classification based on the symmetry analysis, analytic approach, and the quantum Monte Carlo simulations. All these analysis show that our model exhibit a non-Fermi liquid (NFL) physics, a gapless fermionic system lying beyond the conventional Fermi liquid picture.

cond-mat.str-el↗

arXiv2021

Superuniversality from disorder at two-dimensional topological phase transitions

We investigate the effects of quenched randomness on topological quantum phase transitions in strongly interacting two-dimensional systems. We focus first on transitions driven by the condensation of a subset of fractionalized quasiparticles (`anyons') identified with `electric charge' excitations of a phase with intrinsic topological order. All other anyons have nontrivial mutual statistics with the condensed subset and hence become confined at the anyon condensation transition. Using a combination of microscopically exact duality transformations and asymptotically exact real-space renormalization group techniques applied to these two-dimensional disordered gauge theories, we argue that the resulting critical scaling behavior is `superuniversal' across a wide range of such condensation transitions, and is controlled by the same infinite-randomness fixed point as that of the 2D random transverse-field Ising model. We validate this claim using large-scale quantum Monte Carlo simulations that allow us to extract zero-temperature critical exponents and correlation functions in (2+1)D disordered interacting systems. We discuss generalizations of these results to a large class of ground-state and excited-state topological transitions in systems with intrinsic topological order as well as those where topological order is either protected or enriched by global symmetries. When the underlying topological order and the symmetry group are Abelian, our results provide prototypes for topological phase transitions between distinct many-body localized phases.

cond-mat.str-el↗

arXiv2020

Many-Body Invariants for Chern and Chiral Hinge Insulators

We construct new many-body invariants for 2d Chern and 3d chiral hinge insulators, which are characterized by quantized pumping of dipole and quadrupole moments. The invariants that we devise are written entirely in terms of many-body ground state wavefunctions on a torus geometry with a set of unitary operators. We provide a number of supporting evidences for our invariants via topological field theory interpretation, adiabatic pumping argument, and direct mapping to free-fermion band indices. We finally confirm our invariants by numerical computations including infinite density matrix renormalization group on a quasi-one-dimensional system. The many-body invariants therefore explicitly encircle several different pillars of theoretical descriptions of topological phases.

cond-mat.str-el↗

arXiv2019

Many-Body Order Parameters for Multipoles in Solids

We propose many-body order parameters for bulk multipoles in crystalline systems, which originate from the non-trivial topology of the nested Wilson loop spectrum. The many-body order parameters are designed to measure multipolar charge distribution in a crystalline unit cell, and they match the localized corner charge originating from the multipoles. We provide analytic arguments and numerical proof for the order parameters. Furthermore, we show that the many-body order parameters faithfully measure the physical multipole moments even when the symmetries quantizing multipoles are lost and thus the nested Wilson loop spectrum does not exactly reproduce the physical multipole moments.

cond-mat.str-el↗

arXiv2018

Particle-Hole Mirror Symmetries around the Half-Filled Shell: The Quantum Numbers and Algebraic Structure of Composite Fermions

Composite fermions (CFs) of the fractional quantum Hall effect are described as spherical products of electron and vortex spinors, built from underlying L=1/2 ladder operators aligned so that the spinor angular momenta Le and Lv are maximal. We identify the CF's quantum numbers as the angular momentum L in (L_e L_v)L, its magnetic projection m_L, the electron number N, with L_v={N-1)/2, and magnetic ν-spin, m_ν=L_e-L_v. Translationally invariant FQHE states are formed by filling p subshells with their respective CFs, in order of ascending L for fixed L_e and L_v, beginning with the lowest allowed value, L=|m_ν|. We show that this wave function has an exactly equivalent hierarchical form. FQHE states can be grouped into ν-spin multiplets mirror symmetric around m_ν=0, with N held constant. Electron particle-hole conjugation with respect to this vacuum is identified as the mirror symmetry relating FQHE states of the same N but distinct fillings ν= p/(2p+1} and p/( 2p-1). Alternatively, mirror symmetric ν-spin multiplets can be constructed in which the magnetic field strength is held fixed: the valence states are electron particle-vortex hole excitations. Particle-hole symmetry -- relating the N-particle FQHE state of filling ν=p/(2p+1} to the $\bar{N}$-particle state of filling {p+1)/(2p+1} -- is shown to be equivalent to electron-vortex exchange. In this construction $\bar{N}$-N CFs of the higher density state occupy an extra zero-mode subshell. We link this structure, familiar from supersymmetric quantum mechanics, to the CF Pauli Hamiltonian, which we show is isospectral, quadratic in the ν-spin raising and lowering operators, and four-fold degenerate. On linearization, it takes a Dirac form similar to that found in the integer quantum Hall effect (IQHE).

cond-mat.str-el↗

arXiv2017

Universal crossover from ground state to excited-state quantum criticality

We study the nonequilibrium properties of a nonergodic random quantum chain in which highly excited eigenstates exhibit critical properties usually associated with quantum critical ground states. The ground state and excited states of this system belong to different universality classes, characterized by infinite-randomness quantum critical behavior. Using strong-disorder renormalization group techniques, we show that the crossover between the zero and finite energy density regimes is universal. We analytically derive a flow equation describing the unitary dynamics of this isolated system at finite energy density from which we obtain universal scaling functions along the crossover.

cond-mat.dis-nn↗

arXiv2016

The Neutral Excitations in the Gaffnian State

We study a model fractional quantum Hall (FQH) wavefunction called the Gaffnian state, which is believed to represent a gapless, strongly correlated state that is very different from conventional metals. To understand this exotic gapless state better, we provide a representation based on work of Halperin in which the pairing structure of the Gaffnian state becomes more explicit. We employ the single-mode approximation introduced by Girvin, MacDonald, and Platzman (GMP), here extended to three-body interactions, in order to treat a neutral collective exitation mode in order to clarify the physical origin of the gaplessness of the Gaffnian state. We discuss approaches to extract systematically the relevant physics in the long-distance, large-electron-number limit of FQH states using numerical calculations with relatively few electrons. In an appendix, we provide second quantized expressions for many-body Haldane pseudopotentials in various geometries including the plane, sphere, cylinder, and the torus based on the proper definition of the relative angular momentum.

cond-mat.str-el↗