By utilizing biorthogonal bases, we develop a comprehensive framework for studying dynamical quantum phase transitions in non-Hermitian systems. With the help of previously overlooked associated state, define automatically normalized Loschmidt echo. This approach is capable handling arbitrary systems with complex eigenvalues and naturally eliminates negative value rate obtained without bases. Taking Su-Schrieffer-Heeger model as concrete example, $1/2$ change topological order parameter...

We present a comprehensive numerical study of microscopic model the fractional quantum Hall system at filling fraction $\ensuremath{\nu}=5∕2$, based on disk geometry. Our includes Coulomb interaction and semirealistic confining potential. also mix in three-body some cases to help elucidate physics. obtain phase diagram, discuss conditions under which ground state can be described by Moore-Read state, its competition with neighboring stripe phases. quasihole excitations edge Moore-Read-like...

The interplay of interactions, symmetries, and gauge fields usually leads to intriguing quantum many-body phases. To explore the nature emerging phases, we study a Rabi triangle system as an elementary building block for synthesizing artificial magnetic field. We develop analytical approach rich phase diagram associated criticality. Of particular interest is emergence chiral-coherent phase, which breaks both ${\mathbb{Z}}_{2}$ chiral symmetry. In this photons flow unidirectionally chirality...

We show through both theoretical arguments and numerical calculations that graphene discerns an unconventional sequence of quantized Hall conductivity, when subject to magnetic fields (B) strain. The latter produces time-reversal symmetric pseudo/axial (b). single-electron spectrum is composed two interpenetrating sets Landau levels (LLs), located at $\pm \sqrt{2 n |b \pm B|}$, $n=0, 1, 2, \cdots$. For $b>B$, these LLs have opposite \emph{chiralities}, resulting in {\em oscillating}...

We generalize the notion of Haldane pseudopotentials to anisotropic fractional quantum Hall (FQH) systems that are physically realized, e.g., in tilted magnetic field experiments or band structures. This formalism allows us expand any translation-invariant interaction over a complete basis, and directly reveals intrinsic metric incompressible FQH fluids. show purely give rise new types bound states for small particle clusters infinite plane, can be used as diagnostic nematic order. also...

We present comprehensive results on the edge-mode velocities in a quantum Hall droplet with realistic interaction and confinement at various filling fractions. demonstrate that charge-mode velocity scales roughly valence Landau level fraction Coulomb energy corresponding level. At nu = 5/2, stark difference between bosonic fermionic neutral-mode can manifest itself thermal smearing of non-Abelian quasiparticle interference. estimate dependence coherence temperature confining potential...

Recently, quantum Hall interface has become a popular subject of research; distinct from that the edge, which is constrained by external background confinement, freedom to move, likely towards string-like state. In disk geometry, it was known energy an extra correction due its curvature depends on size disk. this work, we analytically calculate integer cone surface advantage more easily adjustable. By tuning length and angle parameter $\beta$, analyze dependence verify geometric correction....

Universal chiral Luttinger liquid behavior has been predicted for fractional quantum Hall edge states, but so far not observed experimentally in semiconductor-based two-dimensional electron gases. One likely cause of this absence universality is the generic occurrence reconstruction such systems, which result a competition between confinement potential and Coulomb repulsion. We show that due to completely different mechanism confinement, can be avoided graphene, allows observation universality.

We investigate fast rotating quasi-two-dimensional dipolar Fermi gases in the quantum Hall regime. By tuning direction of dipole moments with respect to $z$ axis, dipole-dipole interaction becomes anisotropic $x$-$y$ plane. For a soft confining potential we find that, as tilt angle moments, system evolves from $\ensuremath{\nu}=1/3$ Laughlin state dipoles being polarized along axis series ground states characterized by distinct mean total angular momentum, and finally an integer state....

We analytically derived the effective two-body interaction for a finite thickness quantum Hall system with harmonic perpendicular confinement and an in-plane magnetic field. The anisotropic in lowest Landau level (LLL) first (1LL) are expanded basis of generalized pseudopotentials (PPs), we analyze how coefficients some prominent isotropic PPs depend on sample strength also investigate stability topological states, especially Laughlin state its emergent guiding center metric, which can now...

We study the edge-mode excitations of a fractional quantum Hall droplet by expressing edge state wavefunctions as linear combinations Jack polynomials with negative parameter. show that exact diagonalization within subspace can be used to generate chiral excitation spectrum in Laughlin phase and Moore-Read realistic Coulomb interaction. The truncation technique for simplifies procedure extract reliably velocities, which avoids otherwise complicated analysis full contains both bulk...

We present a numerical study of fractional quantum Hall liquid at Landau-level filling factor $\ensuremath{\nu}=2/3$ in microscopic model including long-range Coulomb interaction and edge confining potential based on the disk geometry. find that ground state is accurately described by particle-hole conjugate $\ensuremath{\nu}=1/3$ Laughlin state. also there are two counterpropagating modes, velocity forward-propagating mode larger than backward-propagating mode. The velocities have opposite...

In fractional quantum Hall systems, quasiparticles of charge can tunnel between the edges at a point contact. Such tunneling (or backscattering) processes contribute to transport and provide information on both statistics involved. Here, we study quasiparticle in Moore-Read state, which charges $e/4$ (non-Abelian) $e/2$ (Abelian) may coexist edge transport. On disk geometry, calculate matrix elements for quasiholes through bulk an attempt understand their relative importance. We find that...

In the presence of mass anisotropy, anisotropic interaction, or in-plane magnetic field, quantum Hall droplets can exhibit shape deformation and an internal geometrical degree freedom. We characterize geometry states by principal component analysis, which is a statistical technique that emphasizes variation in data set. first test method integer droplet with dipole-dipole interaction disk geometry. subsequent application to fractional systems Coulomb torus geometry, we demonstrate analysis...

We study the trapping of Abelian anyons (quasiholes and quasiparticles) by a local potential (e.g., induced an atomic force microscopy tip) in microscopic model fractional quantum Hall liquids with long-range Coulomb interaction edge confining potential. find, particular, that at Laughlin filling fraction $\ensuremath{\nu}=1∕3$, both quasihole quasiparticle states can emerge as ground state system presence As expected, we find has no effect on spectrum liquid, unlike non-Abelian case [X. Wan...

Abstract We develop a numerical method for the time evolution of Gaussian wave packets on flat-band lattices in presence correlated disorder. To achieve this, we introduce to generate random on-site energies with prescribed correlations. verify this one-dimensional (1D) cross-stitch model, and find good agreement analytical results obtained from disorder-dressed equations. This allows us reproduce previous findings, that disorder can mobilize 1D states which would otherwise remain localized....

Generally speaking, for a fractional quantum Hall (FQH) state, the electronic occupation number each Landau orbit could be obtained by numerical methods such as exact diagonalization, density matrix renormalization group, product or algebraic recursive schemes (Jack polynomial). In this paper, we apply Metropolis Monte Carlo method to calculate numbers of several FQH states in cylinder geometry. The convergent more than 40 particles are used verify chiral bosonic edge theory and determine...

For the fast rotating quasi-two-dimensional dipolar fermions in quantum Hall regime, rotational symmetry two-body interaction breaks when dipole moment has an in-plane component that can be tuned by external field. Assuming all dipoles are polarized same direction, we perform numerical diagonalization for finite size systems on a torus. We find while $\ensuremath{\nu}=1/3$ Laughlin state is stable lowest Landau level (LLL), it not first (1LL); instead, most 1LL $\ensuremath{\nu}=2+1/5$...

The neutral fermionic edge mode is essential to the non-Abelian topological property and its experimental detection in ${Z}_{k}$ fractional quantum Hall (FQH) state for $k>1$. Usually, identification of modes a finite size system difficult, especially near region reconstruction, due mixing with bosonic bulk states as well. We study edge-mode excitations Moore-Read (MR) Read-Rezayi (RR) by using Jack polynomials truncated subspace. It found that electron density, detector, has marked...

In a Laughlin fractional quantum Hall state, one- and two-quasihole states can be obtained by diagonalizing the many-body Hamiltonian with trapping potential or, for larger systems, from linear combination of edge Jack polynomials. The quasihole live entirely in subspace lowest-energy branch energy spectrum fixed number orbits, or hard-wall confinement. reduction Hilbert space dimension facilitates study time evolution after, say, removal potential. We explore quench dynamics under harmonic...

By exactly solving the effective two-body interaction for two-dimensional electron system with layer thickness and an in-plane magnetic field, we recently found that can be described by generalized pseudopotentials (PPs) without rotational symmetry.With this pseudopotential description, numerically investigate behavior of fractional quantum Hall (FQH) states both in lowest Landau level (LLL) first (1LL).The enhancements 7/3 FQH state on 1LL a small tilted field are observed when is larger...

Bose-Fermi mixtures in one dimension are studied detail on the basis of an exact solution. Corresponding to three possible choices referecce state quantum inverse scattering method, sets Bethe-ansatz equations derived explicitly. The features ground and low-lying excitations investigated. phase diagram caused by external field chemical potential is obtained.

We study the edge states in graphene presence of a magnetic field perpendicular to plane lattice. Most works done so far discuss either zigzag or armchair considering an isotropic electron hopping. In practice, can have mixture and edges hopping be anisotropic, which is subject this article. predict that mixed smear enhanced local density (LDOS) at E=0 and, on other hand, anisotropic gives rise LDOS edge. The behavior studied using scanning tunneling microscopy (STM) experiments. suggest...