Topological quantum matter is typically associated with gapped phases and edge modes protected by the bulk gap. In contrast, recent work (Phys. Rev. B 104, 075132) proposed intrinsically gapless topological phases that, in one dimension, carry protected edge modes only when the bulk is a gapless Luttinger liquid. The edge modes of such a topological Luttinger liquid (TLL) descend from a nonlocal string order that is forbidden in gapped phases and whose precise form depends on the symmetry class of the system. In this work, we propose a powerful and unbiased entanglement-based smoking gun signature of the TLL. In particular, we show that the entanglement entropy profile of a TLL lacks Friedel oscillations that are invariably present in other gapless one dimensional phases such as ordinary Luttinger liquids, and argue that their absence is closely related to a long-ranged string order which is an intrinsic property of the TLL. Crucially, such a diagnostic is more robust against numerical errors and relatively easier to measure in experiments as it relies on the entanglement entropy rather than entanglement spectrum, unlike the entanglement-based diagnostics of gapped topological phases in one dimension.
Topology in quantum matter is typically associated with gapped phases. For example, in symmetry protected topological (SPT) phases, the bulk energy gap localizes edge modes near the boundary. In this work we identify a new mechanism that leads to topological phases which are not only gapless but where the absence of a gap is essential. These `intrinsically gapless SPT phases' have no gapped counterpart and are hence also distinct from recently discovered examples of gapless SPT phases. The essential ingredient of these phases is that on-site symmetries act in an anomalous fashion at low energi…
Deconfined criticality as intrinsically gapless topological state in one dimension
Institute for Advanced Study in Physics and School of Physics, Zhejiang University（浙江大学物理学院和高等研究院）；Department of Physics, Nanjing University（南京大学物理系）；University of Colorado, Boulder（科罗拉多大学博尔德分校）；Harvard University（哈佛大学）；Department of Physics, University of California, San Diego（加州大学圣地亚哥分校物理系）；Fuzhou University（福州大学）；College of Physics and Information Engineering, Fuzhou University（福州大学物理与信息工程学院）
Motivated by recent progress in crystalline symmetry protected topological (SPT) phases of interacting bosons, we study topological crystalline insulators/superconductors (TCIs) of strongly interacting fermions. We construct a class of intrinsically interacting fermionic TCIs, and show that they are beyond both free-fermion TCIs and bosonic crystalline SPT phases. We also show how these phases can be characterized by symmetry protected gapless fermion modes on the corners/hinges of an open system.
A quantum spin liquid (QSL) is a novel phase of matter with long-range entanglement where localized spins are highly correlated with the vanishing of magnetic order. Such exotic quantum states provide the opportunities to develop new theoretical frameworks for many-body physics and have the potential application in realizing robust quantum computations. Here we show that a gapless QSL can naturally emerge from a deconfined quantum critical point (DQCP), which is originally proposed to describe Landau forbidden continuous phase transition between antiferromagnetic (AFM) and valence-bond solid (…
The one-loop polarization function of graphene has been calculated at zero temperature for arbitrary wavevector, frequency, chemical potential (doping), and band gap. The result is expressed in terms of elementary functions and is used to find the dispersion of the plasmon mode and the static screening within the random phase approximation. At long wavelengths the usual square root behaviour of plasmon spectra for two-dimensional (2D) systems is obtained. The presence of a small (compared to a chemical potential) gap leads to the appearance of a new undamped plasmon mode. At greater values of …
Conventional topological superconductors are fully gapped in the bulk but host gapless Majorana modes on their boundaries. We instead focus on a new class of superconductors, second-order topological superconductors, that have gapped, topological surfaces and gapless Majorana modes instead on lower-dimensional boundaries, i.e., corners of a two-dimensional system or hinges for a three-dimensional system. Here we propose two general scenarios in which second-order topological superconductivity can be realized spontaneously with weak-pairing instabilities. First, we show that $p_x+ip_y$-wave pai…
Fathoming interplay between symmetry and topology of many-electron wave-functions has deepened understanding of quantum many body systems, especially after the discovery of topological insulators. Topology of electron wave-functions enforces and protects emergent gapless excitations, and symmetry is intrinsically tied to the topological protection in a certain class. Namely, unless the symmetry is broken, the topological nature is intact. We show novel interplay phenomena between symmetry and topology in topological phase transitions associated with line-nodal superconductors. The interplay ma…
It is well known that the 3D electronic topological insulator (TI) with charge-conservation and time-reversal symmetry cannot have a trivial insulating surface that preserves symmetry. It is often implicitly assumed that if the TI surface preserves both symmetries then it must be gapless. Here we show that it is possible for the TI surface to be both gapped and symmetry-preserving, at the expense of having surface-topological order. In contrast to analogous bosonic topological insulators, this symmetric surface topological order is intrinsically non-Abelian. We show that the surface-topologica…
Topological states may be protected by a lattice symmetry in a class of topological semi-metals. In three spatial dimensions, the Berry flux around gapless excitations in momentum space defines a chirality concretely, so a protecting symmetry may be referred to as a chiral symmetry. Prime examples include Dirac semi-metal (DSM) in a distorted spinel, BiZnSiO$_4$, protected by a mirror symmetry and DSM in Na$_3$Bi, protected by a rotational symmetry. In these states, topology and a chiral symmetry are intrinsically tied. In this work, we investigate characteristics interplay between a chiral sy…
We construct in the K matrix formalism concrete examples of symmetry enriched topological phases, namely intrinsically topological phases with global symmetries. We focus on the Abelian and non-chiral topological phases and demonstrate by our examples how the interplay between the global symmetry and the fusion algebra of the anyons of a topologically ordered system determines the existence of gapless edge modes protected by the symmetry and that a (quasi)-group structure can be defined among these phases. Our examples include phases that display charge fractionalization and more exotic non-lo…
Recently, it has been found that there exist symmetry-protected topological phases of fermions, which have no realizations in non-interacting fermionic systems or bosonic models. We study the edge states of such an intrinsically interacting fermionic SPT phase in two spatial dimensions, protected by $\mathbb{Z}_4\times\mathbb{Z}_2^T$ symmetry. We model the edge Hilbert space by replacing the internal $\mathbb{Z}_4$ symmetry with a spatial translation symmetry, and design an exactly solvable Hamiltonian for the edge model. We show that at low-energy the edge can be described by a two-component …
We consider cold Rydberg atoms in a one-dimensional optical lattice in the Mott regime with a single atom per site at zero temperature. An external laser drive with Rabi frequency Ωand laser detuning Δ, creates Rydberg excitations whose dynamics is governed by an effective spin-chain model with (quasi) long-range interactions. This system possesses intrinsically a large degree of frustration resulting in a ground-state phase diagram in the (Δ,Ω) plane with a rich topology. As a function of Δ, the Rydberg blockade effect gives rise to a series of crystalline phases commensurate with the optical…
Abelian Chern-Simons theory, characterized by the so-called $K$ matrix, has been quite successful in characterizing and classifying Abelian fractional quantum hall effect (FQHE) as well as symmetry protected topological (SPT) phases, especially for bosonic SPT phases. However, there are still some puzzles in dealing with fermionic SPT(fSPT) phases. In this paper, we utilize the Abelian Chern-Simons theory to study the fSPT phases protected by arbitrary Abelian total symmetry $G_f$. Comparing to the bosonic SPT phases, fSPT phases with Abelian total symmetry $G_f$ has three new features: (1) it…
