The Nieh-Yan anomaly is the anomalous breakdown of chiral U(1) symmetry caused by interaction between torsion and fermions. We study this from point view torsional Landau levels. It was found that levels are gapless, while their contributions to canceled, except those lowest Hence, dimension effectively reduced $(3+1)$-dimensional $(1+1)$-dimensional. further show coefficient free-energy density in $(1+1)$ dimensions. Especially, at finite temperature, thermal proportional central charge....

Motivated by symmetry-protected topological phases (SPTs) with both spatial symmetry (e.g., lattice rotation) and internal spin rotation), we propose a class of exotic terms, which generalize the well-known Wen-Zee terms quantum Hall systems [X.-G. Wen A. Zee, Phys. Rev. Lett. 69, 953 (1992)]. These generalized are expressed as wedge product connection usual gauge fields (1-form or higher) in various dimensions. In order to probe SPT orders, externally insert twists such domain walls...

Teleportation is a facet where quantum measurements can act as powerful resource in physics, local allow us to steer information nonlocal way. While this has long been established for single Bell pair, the teleportation of many-qubit entangled state using nonmaximally resources presents fundamentally different challenge. Here, we investigate tangible protocol teleporting long-range surface-code elementary and its stability presence coherent errors that weaken entanglement. We relate...

We propose a diagnostic tool for detecting non-trivial symmetry protected topological (SPT) phases by group $G$ in 2+1 dimensions. Our method is based on directly studying the 1+1-dimensional anomalous edge conformal field theory (CFT) of SPT phases. claim that if CFT an phase, then there must be obstruction to cutting it open. This manifests in-existence boundary states preserves both and global $G$. discuss relation between edgeability, ability find consistent state, gappability, gap out...

We study the entanglement entropy between (possibly distinct) topological phases across an interface using Abelian Chern-Simons description with boundary conditions (TBCs) at interface. From a microscopic point of view, these TBCs correspond to turning on particular gapping interactions edge modes However, in studying continuum description, we must confront problem non-factorization Hilbert space, which is standard property gauge theories. carefully define by extended space construction...

Classification of the nonequilibrium quantum many-body dynamics is a challenging problem in condensed matter physics and statistical mechanics. In this work, we study basic question that whether ($1+1$) dimensional conformal field theory (CFT) stable or not under periodic driving with $N$ noncommuting Hamiltonians. Previous works showed Floquet (or periodically driven) CFT driven by certain ${SL}_{2}$ deformed Hamiltonians exhibit both nonheating (stable) heating (unstable) phases. show...

We study unusual gapped topological phases where they admit \mathbb{Z}_N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>ℤ</mml:mi><mml:mi>N</mml:mi></mml:msub></mml:math> fractional excitations in the same manner as topologically ordered phases, yet their ground state degeneracy depends on local geometry of system. Placing such 2D lattice, composed an arbitrary connected graph and 1D line, we find that fusion rules quasiparticle are described by...

Torsion can cause various anomalies in dimensions, including the $(3+1)$-dimensional $[(3+1)\mathrm{D}]$ Nieh-Yan anomaly, $\left(2+1\right)\text{D}$ Hughes-Leigh-Fradkin (HLF) parity and $\left(3+1\right)\mathrm{D}$, $\left(1+1\right)\mathrm{D}$ chiral energy-momentum anomaly. We study these from Hamiltonian approach. derive anomaly single-body Hamiltonian. then show how other torsional be related to a straightforward way. Finally, $\left(3+1\right)\mathrm{D}$ are obtained HLF effective...

At a fixed magnetic filling fraction, fractional quantum Hall states may display plethora of interaction-induced competing phases. Effective Chern-Simons theories have suggested the existence multiple short-range entangled phases also at integer plateaus. Among these, bosonic phase has been proposed with edge modes carrying representations based on ${E}_{8}$ exceptional Lie algebra. Through theoretical coupled-wire construction, we provide an explicit microscopic model for this Abelian...

Abstract Time crystals are a dynamical phase of periodically driven quantum many-body systems where discrete time-translation symmetry is broken spontaneously. Time-crystallinity however subtly requires also spatial order, ordinarily related to further symmetries, such as spin-flip when the order ferromagnetic. Here we define topologically ordered time crystals, time-crystalline borne out intrinsic topological order—a particularly robust form that no symmetry. We show localization can...

Teleportation is a facet where quantum measurements can act as powerful resource in physics, local allow to steer information non-local way. While this has long been established for single Bell pair, the teleportation of fault-tolerant logical qubit presents fundamentally different challenge it requires many-qubit state. Here we investigate tangible protocol teleporting long-range entangled surface code state using elementary and its stability presence tunable coherent errors. We relate...

Topologically ordered phases of matter can be characterized by the presence a universal, constant contribution to entanglement entropy known as topological (TEE). The TEE been calculated for Abelian via "cut-and-glue" approach treating cut physical cut, coupling resulting gapless edges with explicit tunneling terms, and computing between two edges. We provide first step towards extending this methodology non-Abelian phases, focusing on generalized Moore-Read (MR) fractional quantum Hall...

The electronic transport properties of charge-ordered Bi0.4Ca0.6MnO3 films grown on a (110) SrTiO3 substrate are experimentally studied. Special attention has been paid to the Hall effect around charge-ordering (CO) transition. charge carriers found be electron-like, and carrier density n exhibits significant change upon CO transition: it is nearly constant above transition temperature Tco, ∼0.36 electrons/Mn, reduces with decrease below Tco following formula , an activation energy EH ∼0.13...

Based on the supersymmetric quantum mechanical approach, we have systematically studied both $U\left(1\right)$ gauge anomaly and diffeomorphism in Weyl systems with torsion, curvature external electromagnetic fields. These anomalies relate to chiral current (or current) non-conservation energy-momentum energy-momentum) non-conservation, respectively, which can be applied $^{3}\text{He-A}$ phase, superconductors semimetals dislocations disclinations. In sharp difference other anomalies, there...

We study the effective action of hydrostatic response to torsion in absence spin connections gapped $\left(2+1\right)$-dimensional topological phases. In previous studies, a torsional Chern-Simons term with temperature-squared ($T^2$) coefficient was proposed as an alternative describe thermal Hall effect idea balancing diffusion heat by field. However, question remains whether this leads local bulk which is not suppressed gap. our action, we show that $T^2$ invariant under variations up...

Symmetry-protected and symmetry-enriched topological (SPT/SET) phases in three dimensions are quantum systems that support non-trivial two-dimensional surface states. These states develop finite excitation energy gaps when the relevant symmetries broken. On other hand, one-dimensional gapless modes can populate along interfaces separate adjacent gapped domains with distinct symmetry-breaking orders. A strip pattern general reduces low-energy SPT/SET degrees of freedom onto a 2D array 1D...

We define topological time crystals, a dynamical phase of periodically driven quantum many-body systems capturing the coexistence intrinsic order with spontaneous breaking discrete time-translation symmetry. show that localization can stabilize this against generic perturbations and establish some its key features signatures, including dynamical, time-crystal form perimeter law for order. link ordinary crystals through three complementary perspectives: higher-form symmetries,...