arXiv subjects

Chenjie Wang

Publications and source records attributed to Chenjie Wang.

49 records · Page 3Linked to original sources

arXiv2015

Bulk-boundary correspondence for three-dimensional symmetry-protected topological phases

We derive a bulk-boundary correspondence for three-dimensional (3D) symmetry-protected topological (SPT) phases with unitary symmetries. The correspondence consists of three equations that relate bulk properties of these phases to properties of their gapped, symmetry-preserving surfaces. Both the bulk and surface data appearing in our correspondence are defined via a procedure in which we gauge the symmetries of the system of interest and then study the braiding statistics of excitations of the resulting gauge theory. The bulk data is defined in terms of the statistics of bulk excitations, while the surface data is defined in terms of the statistics of surface excitations. An appealing property of this data is that it is plausibly complete in the sense that the bulk data uniquely distinguishes each 3D SPT phase, while the surface data uniquely distinguishes each gapped, symmetric surface. Our correspondence applies to any 3D bosonic SPT phase with finite Abelian unitary symmetry group. It applies to any surface that (1) supports only Abelian anyons and (2) has the property that the anyons are not permuted by the symmetries.

cond-mat.str-el↗

arXiv2015

Fluctuation relations for spin currents

The fluctuation theorem establishes general relations between transport coefficients and fluctuations in nonequilibrium systems. Recently there was much interest in quantum fluctuation relations for electric currents. Since charge carriers also carry spin, it is important to extend the fluctuation theorem to spin currents. We use the principle of microscopic reversibility to derive such theorem. As a consequence, we obtain a family of relations between transport coefficients and fluctuations of spin currents. We apply the relations to the spin Seebeck effect and rectification of spin currents. Our relations do not depend on a microscopic model and hence can be used to test the validity of theoretical approximations in spin-transport problems.

cond-mat.stat-mech↗

arXiv2015

Topological invariants for gauge theories and symmetry-protected topological phases

We study the braiding statistics of particle-like and loop-like excitations in 2D and 3D gauge theories with finite, Abelian gauge group. The gauge theories that we consider are obtained by gauging the symmetry of gapped, short-range entangled, lattice boson models. We define a set of quantities --- called {\it topological invariants} --- that summarize some of the most important parts of the braiding statistics data for these systems. Conveniently, these invariants are always Abelian phases, even if the gauge theory supports excitations with non-Abelian statistics. We compute these invariants for gauge theories obtained from the exactly soluble group cohomology models of Chen, Gu, Liu and Wen, and we derive two results. First, we find that the invariants take different values for every group cohomology model with finite, Abelian symmetry group. Second, we find that these models exhaust all possible values for the invariants in the 2D case, and we give some evidence for this in the 3D case. The first result implies that every one of these models belongs to a distinct SPT phase, while the second result suggests that these models may realize all SPT phases. These results support the group cohomology classification conjecture for SPT phases in the case where the symmetry group is finite, Abelian, and unitary.

cond-mat.str-el↗

arXiv2014

Braiding statistics of loop excitations in three dimensions

While it is well known that three dimensional quantum many-body systems can support non-trivial braiding statistics between particle-like and loop-like excitations, or between two loop-like excitations, we argue that a more fundamental quantity is the statistical phase associated with braiding one loop $α$ around another loop $β$, while both are linked to a third loop $γ$. We study this three-loop braiding in the context of $(\mathbb{Z}_N)^K$ gauge theories which are obtained by gauging a gapped, short-range entangled lattice boson model with $(\mathbb{Z}_N)^K$ symmetry. We find that different short-range entangled bosonic states with the same $(\mathbb{Z}_N)^K$ symmetry (i.e. different symmetry-protected topological phases) can be distinguished by their three-loop braiding statistics.

cond-mat.str-el↗

arXiv2014

Weak symmetry breaking in two dimensional topological insulators

We show that there exist two dimensional (2D) time reversal invariant fractionalized insulators with the property that both their boundary with the vacuum and their boundary with a topological insulator can be fully gapped without breaking time reversal or charge conservation symmetry. This result leads us to an apparent paradox: we consider a geometry in which a disk-like region made up of a topological insulator is surrounded by an annular strip of a fractionalized insulator, which is in turn surrounded by the vacuum. If we gap both boundaries of the strip, we naively obtain an example of a gapped interface between a topological insulator and the vacuum that does not break any symmetries -- an impossibility. The resolution of this paradox is that this system spontaneously breaks time reversal symmetry in an unusual way, which we call \emph{weak symmetry breaking}. In particular, we find that the only order parameters that are sensitive to the symmetry breaking are nonlocal operators that describe quasiparticle tunneling processes between the two edges of the strip; expectation values of local order parameters vanish exponentially in the limit of a wide strip. Also, we find that the symmetry breaking in our system comes with a ground state degeneracy, but this ground state degeneracy is topologically protected, rather than symmetry protected. We show that this kind of symmetry breaking can also occur at the edge of 2D fractional topological insulators.

cond-mat.str-el↗

arXiv2014

Fluctuation theorems without time-reversal symmetry

Fluctuation theorems establish deep relations between observables away from thermal equilibrium. Until recently, the research on fluctuation theorems was focused on time-reversal-invariant systems. In this review we address some newly discovered fluctuation relations that hold without time-reversal symmetry, in particular, in the presence of an external magnetic field. One family of relations connects non-linear transport coefficients in the opposite magnetic fields. Another family relates currents and noises at a fixed direction of the magnetic field in chiral systems, such as the edges of some quantum Hall liquids. We review the recent experimental and theoretical research, including the controversy on the microreversibility without time-reversal symmetry, consider the applications of fluctuation theorems to the physics of topological states of matter, and discuss open problems.

cond-mat.stat-mech↗

arXiv2013

Chirality, causality, and fluctuation-dissipation theorems in non-equilibrium steady states

Edges of some quantum Hall liquids and a number of other systems exhibit chiral transport: excitations can propagate in one direction only, e.g., clockwise. We derive a family of fluctuation-dissipation relations in non-equilibrium steady states of such chiral systems. The theorems connect nonlinear response with fluctuations far from thermal equilibrium and hold only in case of chiral transport. They can be used to test chiral or non-chiral character of the system.

cond-mat.stat-mech↗

arXiv2012

Fluctuation-dissipation theorem for chiral systems in non-equilibrium steady states

We consider a three-terminal system with a chiral edge channel connecting the source and drain terminals. Charge can tunnel between the chiral edge and a third terminal. The third terminal is maintained at a different temperature and voltage than the source and drain. We prove a general relation for the current noises detected in the drain and third terminal. It has the same structure as an equilibrium fluctuation-dissipation relation with the nonlinear response in place of the linear conductance. The result applies to a general chiral system and can be useful for detecting "upstream" modes on quantum Hall edges.

cond-mat.stat-mech↗

arXiv2011

Rectification in Y-junctions of Luttinger liquid wires

We investigate rectification of a low-frequency ac bias in Y-junctions of one-channel Luttinger liquid wires with repulsive electron interaction. Rectification emerges due to three scatterers in the wires. We find that it is possible to achieve a higher rectification current in a Y-junction than in a single wire with an asymmetric scatterer at the same interaction strength and voltage bias. The rectification effect is the strongest in the absence of the time-reversal symmetry. In that case, the maximal rectification current can be comparable with the total current $\sim e^2V/h$ even for low voltages, weak scatterers and modest interaction strength. In a certain range of low voltages, the rectification current can grow as the voltage decreases. This leads to a bump in the $I$-$V$ curve.

cond-mat.mes-hall↗

arXiv2010

Identification of 331 quantum Hall states with Mach-Zehnder interferometry

It has been shown recently that non-Abelian states and the spin-polarized and unpolarized versions of the Abelian 331 state may have identical signatures in Fabry-Pérot interferometry in the quantum Hall effect at filling factor 5/2. We calculate the Fano factor for the shot noise in a Mach-Zehnder interferometer in the 331 states and demonstrate that it differs from the Fano factor in the proposed non-Abelian states. The Fano factor depends periodically on the magnetic flux through the interferometer. Its maximal value is $2\times 1.4e$ for the 331 states with a symmetry between two flavors of quasiparticles. In the absence of such symmetry the Fano factor can reach $2\times 2.3e$. On the other hand, for the Pfaffian and anti-Pfaffian states the maximal Fano factor is $2\times 3.2e$. The period of the flux dependence of the Fano factor is one flux quantum. If only quasiparticles of one flavor can tunnel through the interferometer then the period drops to one half of the flux quantum. We also discuss transport signatures of a general Halperin state with the filling factor $2+k/(k+2)$.

cond-mat.mes-hall↗

arXiv2010

Transport in line junctions of $ν=5/2$ quantum Hall liquids

We calculate the tunneling current through long line junctions of a $ν=5/2$ quantum Hall liquid and i) another $ν=5/2$ liquid, ii) an integer quantum Hall liquid and iii) a quantum wire. Momentum resolved tunneling provides information about the number, propagation directions and other features of the edge modes and thus helps distinguish several competing models of the 5/2 state. We investigate transport properties of two proposed Abelian states: $K=8 state and 331 state, and four possible non-Abelian states: Pfaffian, edge-reconstructed Pfaffian, and two versions of the anti-Pfaffian state. We also show that the non-equilibrated anti-Pfaffian state has a different resistance from other proposed states in the bar geometry.

cond-mat.mes-hall↗

arXiv2007

First-principles study of the lattice and electronic structures of TbMn$_2$O$_5$

The structural, electronic and lattice dielectric properties of multiferroic TbMn$_2$O$_5$ are investigated using density functional theory within the generalized gradient approximation (GGA). We use collinear spin approximations and ignore the spin-orbit coupling. The calculated structural parameters are in excellent agreement with the experiments. We confirm that the ground state structure of TbMn$_2$O$_5$ is of space group $Pb2_1m$, allowing polarizations along the b-axis. The spontaneous electric polarization is calculated to be 1187 $nC\cdot$cm$^{-2}$. The calculated zone-center optical phonons frequencies and the oscillator strengths of IR phonons agree very well with the experimental values. We then derive an effective Hamiltonian to explain the magnetically-induced ferroelectricity in this compound. Our results strongly suggest that the ferroelectricity in TbMn$_2$O$_5$ is driven by the magnetic ordering that breaks the the inversion symmetry, without invoking the spin-orbit coupling.

cond-mat.mtrl-sci↗

arXiv2007

Ferroelectricity driven by the non-centrosymmetric magnetic ordering in multiferroic TbMn_2O_5: a first-principles study

The ground state structural, electronic and magnetic properties of multiferroic TbMn$_2$O$_5$ are investigated via first-principles calculations. We show that the ferroelectricity in TbMn$_2$O$_5$ is driven by the non-centrosymmetric magnetic ordering, without invoking the spin-orbit coupling and non-collinear spins. The {\it intrinsic} electric polarization in this compound is calculated to be 1187 $nC\cdot$ cm$^{-2}$, an order of magnitude larger than previously thought.

cond-mat.mtrl-sci↗