arXiv subjects

Peng Ye

Publications and source records attributed to Peng Ye.

214 records · Page 12Linked to original sources

arXiv2015

Vortex-line condensation in three dimensions: A physical mechanism for bosonic topological insulators

Bosonic topological insulators (BTI) in three dimensions are symmetry-protected topological phases (SPT) protected by time-reversal and boson number conservation {symmetries}. BTI in three dimensions were first proposed and classified by the group cohomology theory which suggests two distinct root states, each carrying a $\mathbb{Z}_2$ index. Soon after, surface anomalous topological orders were proposed to identify different root states of BTI, which even leads to a new BTI root state beyond the group cohomology classification. In this paper, we propose a universal physical mechanism via \textit{vortex-line condensation} {from} a 3d superfluid to achieve all {three} root states. It naturally produces bulk topological quantum field theory (TQFT) description for each root state. Topologically ordered states on the surface are \textit{rigorously} derived by placing TQFT on an open manifold, which allows us to explicitly demonstrate the bulk-boundary correspondence. Finally, we generalize the mechanism to $Z_N$ symmetries and discuss potential SPT phases beyond the group cohomology classification.

cond-mat.str-el↗

arXiv2014

$U(1)\times U(1)$ Symmetry Protected Topological Order in Gutzwiller Wave Functions

Gutzwiller projection is a way to construct many-body wave functions that could carry topological order or symmetry protected topological (SPT) order. However, an important issue is to determine whether or not a given Gutzwiller-projected wave functions (GWF) carries a non-trivial SPT order, and which SPT order is carried by the wavefunction. In this paper, we numerically study the SPT order in a spin $S = 1$ GWF on the Kagome lattice. Using the standard Monte Carlo method, we directly confirm that the GWF has (1) gapped bulk with short-range correlations, (2) a trivial topological order via nondegenerate ground state, and zero topological entanglement entropy, (3) a non-trivial $U(1)\times U(1)$ SPT order via the Hall conductances of the protecting $U(1)\times U(1)$ symmetry, and (4) symmetry protected gapless boundary. This represents numerical evidence of continuous symmetry protected topological order in two-dimensional bosonic lattice systems.

cond-mat.str-el↗

arXiv2014

Free-fermion Entanglement Spectrum through Wannier Interpolation

Quantum Entanglement plays an ubiquitous role in theoretical physics, from the characterization of novel phases of matter to understanding the efficacy of numerical algorithms. As such, there have been extensive studies on the entanglement spectrum (ES) of free-fermion systems, particularly in the relation between its spectral flow and topological charge pumping. However, far less has been studied about the \emph{spacing} between adjacent entanglement eigenenergies, which affects the truncation error in numerical computations involving Matrix Product States (MPS) or Projected Entangled-Pair States (PEPS). In this paper, we shall hence derive asymptotic bounds for the ES spacings through an interpolation argument that utilizes known results on Wannier function decay. For translation invariant systems, the Entanglement energies are shown to decay at a rate monotonically related to the complex gap between the filled and occupied bands. This interpolation also demonstrates the one-to-one correspondence between the ES and the edge states. Our results also provide asymptotic bounds for the eigenvalue distribution of certain types of Block Toeplitz matrices common in physics, even for those not arising from entanglement calculations.

cond-mat.quant-gas↗

arXiv2014

A random forest system combination approach for error detection in digital dictionaries

When digitizing a print bilingual dictionary, whether via optical character recognition or manual entry, it is inevitable that errors are introduced into the electronic version that is created. We investigate automating the process of detecting errors in an XML representation of a digitized print dictionary using a hybrid approach that combines rule-based, feature-based, and language model-based methods. We investigate combining methods and show that using random forests is a promising approach. We find that in isolation, unsupervised methods rival the performance of supervised methods. Random forests typically require training data so we investigate how we can apply random forests to combine individual base methods that are themselves unsupervised without requiring large amounts of training data. Experiments reveal empirically that a relatively small amount of data is sufficient and can potentially be further reduced through specific selection criteria.

cs.CL↗

arXiv2014

Detecting Structural Irregularity in Electronic Dictionaries Using Language Modeling

Dictionaries are often developed using tools that save to Extensible Markup Language (XML)-based standards. These standards often allow high-level repeating elements to represent lexical entries, and utilize descendants of these repeating elements to represent the structure within each lexical entry, in the form of an XML tree. In many cases, dictionaries are published that have errors and inconsistencies that are expensive to find manually. This paper discusses a method for dictionary writers to quickly audit structural regularity across entries in a dictionary by using statistical language modeling. The approach learns the patterns of XML nodes that could occur within an XML tree, and then calculates the probability of each XML tree in the dictionary against these patterns to look for entries that diverge from the norm.

cs.CL↗

arXiv2014

Position momentum Duality in the Entanglement Spectrum of Free Fermions

We propose an exact equivalence between the entanglement spectra of two completely different free-fermion systems at zero temperature. This equivalence follows from a position-momentum duality where the physical roles of the occupied band and real space projectors are exchanged. We examine the physical consequences of this duality in multi-band models, and as an example also physically motivate the equivalence of the entanglement spectrum of a real space partitioned two-band topological insulator with that of a bilayer Fermi gas with an interlayer partition. This duality has an interesting relation with the Wannier Spectrum in the high-temperature limit, and can also be extended to other basis-independent physical quantities like particle-number fluctuations.

cond-mat.str-el↗

arXiv2014

Sign structure and ground state properties for a spin-$S$ $t$-$J$ chain

The antiferromagnetic Heisenberg spin chain of odd spin $S$ is in the Haldane phase with several defining physical properties, such as thermodynamical ground-state degeneracy, symmetry-protected edge states, and nonzero string order parameter. If nonzero hole concentration $δ$ and hole hopping energy $t$ are considered, the spin chain is replaced by a spin-$S$ $t$-$J$ chain. The motivation of this paper is to generalize the discussions of the Haldane phase to the doped spin chain. The \emph{first result} of this paper is that, for the model considered here, the $\mathbb{Z}_2$ sign structure in the usual Ising basis can be totally removed by two consecutive unitary transformations consisting of a spatially local one and a nonlocal one. Direct from the sign structure, the \emph{second result} of this paper is that the Marshall theorem and the Lieb-Mattis theorem for pure spin systems are generalized to the $t$-$J$ chain for arbitrary $S$ and $δ$. A corollary of the theorem provides us with the ground-state degeneracy in the thermodynamic limit. The \emph{third result} of this paper is about the phase diagram. We show that the defining properties of the Haldane phase survive in the small $t/J$ limit. The large $t/J$ phase supports a gapped spin sector with similar properties (ground-state degeneracy, edge state, and string order parameter) of the Haldane chain, although the charge sector is gapless.

cond-mat.str-el↗

arXiv2014

Low-Temperature Pseudogap Phenomenon: Precursor of High-$T_c$ Superconductivity

In this paper, we try to understand the pseudogap phenomenon observed in the cuprate superconductor through a model study. Specifically, we explore the so-called low-temperature pseudogap state by turning off the superconducting off diagonal long range order in an ansatz state for the $t$-$J$ model [New Journal of Physics {\bf 13}, 103039 (2011)]. Besides strong non-Gaussian superconducting fluctuations, the resulting state also exhibits a systematic pseudogap behavior in both spin and charge degrees of freedom, manifested in the uniform spin susceptibility, specific heat, non-Drude resistivity, Nernst effect, as well as the quantum oscillation associated with small Fermi pockets emerging in strong magnetic fields, etc. These anomalous `normal state' properties are found in qualitative consistency with experimental measurements in the cuprates. Such a model study establishes an intrinsic connection between the peculiar pseudogap properties and the non-BCS nature of the superconducting ground state. Critical comparison with other approaches to the doped Mott insulator is also made.

cond-mat.supr-con↗

arXiv2013

Symmetry-protected topological phases with charge and spin symmetries: response theory and dynamical gauge theory in 2D, 3D and the surface of 3D

A large class of symmetry-protected topological phases (SPT) in boson / spin systems have been recently predicted by the group cohomology theory. In this work, we consider SPT states at least with charge symmetry (U(1) or Z$_N$) or spin $S^z$ rotation symmetry (U(1) or Z$_N$) in 2D, 3D, and the surface of 3D. If both are U(1), we apply external electromagnetic field / `spin gauge field' to study the charge / spin response. For the SPT examples we consider (i.e. U$_c$(1)$\rtimes$Z$^T_2$, U$_s$(1)$\times$Z$^T_2$, U$_c$(1)$\times$[U$_s$(1)$\rtimes$Z$_2$]; subscripts $c$ and $s$ are short for charge and spin; Z$^T_2$ and Z$_2$ are time-reversal symmetry and $π$-rotation about $S^y$, respectively), many variants of Witten effect in the 3D SPT bulk and various versions of anomalous surface quantum Hall effect are defined and systematically investigated. If charge or spin symmetry reduces to Z$_N$ by considering charge-$N$ or spin-$N$ condensate, instead of the linear response approach, we gauge the charge/spin symmetry, leading to a dynamical gauge theory with some remaining global symmetry. The 3D dynamical gauge theory describes a symmetry-enriched topological phase (SET), i.e. a topologically ordered state with global symmetry which admits nontrivial ground state degeneracy depending on spatial manifold topology. For the SPT examples we consider, the corresponding SET states are described by dynamical topological gauge theory with topological BF term and axionic $Θ$-term in 3D bulk. And the surface of SET is described by the chiral boson theory with quantum anomaly.

cond-mat.str-el↗

arXiv2013

Constructing symmetric topological phases of bosons in three dimensions via fermionic projective construction and dyon condensation

Recently, there is a considerable study on gapped symmetric phases of bosons that do not break any symmetry. Even without symmetry breaking, the bosons can still be in many exotic new states of matter, such as symmetry-protected trivial (SPT) phases which are short-range entangled and symmetry-enriched topological (SET) phases which are long-range entangled. It is well-known that non-interacting fermionic topological insulators are SPT states protected by time-reversal symmetry and U(1) fermion number conservation symmetry. In this paper, we construct three-dimensional exotic phases of bosons with time-reversal symmetry and boson number conservation U(1) symmetry by means of fermionic projective construction. We first construct an algebraic bosonic insulator which is a symmetric bosonic state with an emergent U(1) gapless gauge field. We then obtain many gapped bosonic states that do not break the time-reversal symmetry and boson number conservation via proper dyon condensations. We identify the constructed states by calculating the allowed electric and magnetic charges of their excitations, as well as the statistics and the symmetric transformation properties of those excitations. This allows us to show that our constructed states can be trivial SPT states (i.e. trivial Mott insulators of bosons with symmetry), non-trivial SPT states (i.e. bosonic topological insulators) and SET states (i.e. fractional bosonic topological insulators). In non-trivial SPT states, the elementary monopole (carrying zero electric charge but unit magnetic charge) and elementary dyon (carrying both unit electric charge and unit magnetic charge) are fermionic and bosonic, respectively. In SET states, intrinsic excitations may carry fractional charge.

cond-mat.str-el↗

arXiv2013

Monopoles, confinement and charge localization in the t-J model with dilute holes

We present a quantum field theoretic description on the t$-$J model on a square lattice with dilute holes (i.e. near half-filling), based on the compact mutual Chern-Simons gauge theory. We show that, due to the presence of non-perturbative monopole plasma configuration from the antiferromagnetic background, holons (carrying electric charge) are linearly confined and strongly localized even without extrinsic disorder taken into account. Accordingly, the translation symmetry is spontaneously broken at ground state. Such an exotic localization is distinct from Anderson localization and essentially rooted in intrinsic Mott physics of the t$-$J model. Finally, a finite-temperature phase diagram is proposed. The metal-insulator transition observed in in-plane resistivity measurement is identified to a confinement-deconfinement transition from the perspective of gauge theory. The transition is characterized by the order parameter "Polyakov-line".

cond-mat.str-el↗

arXiv2013

Projective construction of two-dimensional symmetry-protected topological phases with U(1), SO(3), or SU(2) symmetries

We propose a general approach to construct symmetry protected topological (SPT) states i.e the short-range entangled states with symmetry) in 2D spin/boson systems on lattice. In our approach, we fractionalize spins/bosons into different fermions, which occupy nontrivial Chern bands. After the Gutzwiller projection of the free fermion state obtained by filling the Chern bands, we can obtain SPT states on lattice. In particular, we constructed a U(1) SPT state of a spin-1 model, a SO(3) SPT state of a boson system with spin-1 bosons and spinless bosons, and a SU(2) SPT state of a spin-1/2 boson system. By applying the "spin gauge field" which directly couples to the spin density and spin current of $S^z$ components, we also calculate the quantum spin Hall conductance in each SPT state. The projective ground states can be further studied numerically in the future by variational Monte Carlo etc.

cond-mat.str-el↗

arXiv2012

Chiral gauge field and axial anomaly in a Weyl semi-metal

Weyl fermions are two-component chiral fermions in (3+1)-dimensions. When coupled to a gauge field, the Weyl fermion is known to have an axial anomaly, which means the current conservation of the left-handed and right-handed Weyl fermions cannot be preserved separately. Recently, Weyl fermions have been proposed in condensed matter systems named as "Weyl semi-metals". In this paper we propose a Weyl semi-metal phase in magnetically doped topological insulators, and study the axial anomaly in this system. We propose that the magnetic fluctuation in this system plays the role of a "chiral gauge field" which minimally couples to the Weyl fermions with opposite charges for two chiralities. We study the anomaly equation of this sytem and discuss its physical consequences, including one-dimensional chiral modes in a ferromagnetic vortex line, and a novel plasmon-magnon coupling.

cond-mat.str-el↗

arXiv2012

Superconductivity in Mutual Chern-Simons Gauge Theory

In this work, we present a topological characterization of superconductivity in a prototype electron fractionalization model for doped Mott insulators. In this model, spinons and holons are coupled via the mutual Chern-Simons gauge fields. We obtain a low-lying effective description of the collective current fluctuations by integrating out the matter fields, which replaces the conventional Ginzburg-Landau action to describe the generalized rigidity of superconductivity. The superconducting phase coherence is essentially characterized by a topological order parameter related to a Gaussian linking number, and an experiment is proposed to probe this topological property. We further show that a gauge-neutral fermionic mode can naturally emerge in this model, which behaves like a Bogoliubov quasiparticle.

cond-mat.supr-con↗

arXiv2011

Electron fractionalization and unconventional order parameters of the t-J model

In the $t-J$ model, the electron fractionalization is unique due to the non-perturbative phase string effect. We formulated a lattice field theory taking this effect into full account. Basing on this field theory, we introduced a pair of Wilson loops which constitute a complete set of order parameters determining the phase diagram in the underdoped regime. We also established a general composition rule for electric transport expressing the electric conductivity in terms of the spinon and the holon conductivities. The general theory is applied to studies of the quantum phase diagram. We found that the antiferromagnetic and the superconducting phases are dual: in the former, holons are confined while spinons are deconfined, and {\it vice versa} in the latter. These two phases are separated by a novel phase, the so-called Bose-insulating phase, where both holons and spinons are deconfined and the system is electrically insulating.

cond-mat.str-el↗

arXiv2011

Confinement-deconfinement interplay in quantum phases of doped Mott insulators

It is generally accepted that doped Mott insulators can be well characterized by the t-J model. In the t-J model, the electron fractionalization is dictated by the phase string effect. We found that in the underdoped regime, the antiferromagnetic and superconducting phases are dual: in the former, holons are confined while spinons are deconfined, and {\it vice versa} in the latter. These two phases are separated by a novel phase, the so-called Bose-insulating phase, where both holons and spinons are deconfined. A pair of Wilson loops was found to constitute a complete set of order parameters determining this zero-temperature phase diagram. The quantum phase transitions between these phases are suggested to be of non-Landau-Ginzburg-Wilson type.

cond-mat.str-el↗