Entanglement spectrum of a topological phase in one dimension

Pollmann, Frank; Turner, Ari M.; Berg, Erez; Oshikawa, Masaki

doi:10.1103/physrevb.81.064439

Cited by 1,226 publications

(1,753 citation statements)

References 37 publications

Supporting

Mentioning

1,676

Contrasting

Order By: Relevance

“…Following established techniques [116][117][118], let U I denote the action of inversion and U θ ↑/↓ the U(1) symmetries of the upper/lower layer when acting on Schmidt states. A priori, these U have U(1) phase ambiguities, which we will gauge fix as follows.…”

Section: Spin-charge Separationmentioning

confidence: 99%

Competing Abelian and non-Abelian topological orders inν=1/3+1/3quantum Hall bilayers

et al. 2015

View full text Add to dashboard Cite

Bilayer quantum Hall systems, realized either in two separated wells or in the lowest two sub-bands of a wide quantum well, provide an experimentally realizable way to tune between competing quantum orders at the same filling fraction. Using newly developed density matrix renormalization group techniques combined with exact diagonalization, we return to the problem of quantum Hall bilayers at filling ν = 1/3 + 1/3. We first consider the Coulomb interaction at bilayer separation d, bilayer tunneling energy ∆SAS, and individual layer width w, where we find a phase diagram which includes three competing Abelian phases: a bilayer-Laughlin phase (two nearly decoupled ν = 1/3 layers); a bilayer-spin singlet phase; and a bilayer-symmetric phase. We also study the order of the transitions between these phases. A variety of non-Abelian phases have also been proposed for these systems. While absent in the simplest phase diagram, by slightly modifying the interlayer repulsion we find a robust non-Abelian phase which we identify as the "interlayer-Pfaffian" phase. In addition to non-Abelian statistics similar to the Moore-Read state, it exhibits a novel form of bilayer-spin charge separation. Our results suggest that ν = 1/3 + 1/3 systems merit further experimental study. CONTENTS

show abstract

Section: Spin-charge Separationmentioning

confidence: 99%

Competing Abelian and non-Abelian topological orders inν=1/3+1/3quantum Hall bilayers

et al. 2015

View full text Add to dashboard Cite

show abstract

“…That is, two time-reversal twists compose into identity up to a universal phase factor characterizing the underlying SPT order of the state. In 1D, the distinction between different time-reversal SPT phases has been well understood in the matrix product formalism [ [17][18][19][20]. Our discussion is just a reinterpretation of that procedure in terms of local time-reversal symmetry action and time-reversal twists.…”

Section: Introductionmentioning

confidence: 99%

“…II, we discuss the 1D case in terms of matrix product states (MPS) and present a way to insert timereversal fluxes through a 1D ring. In 1D there are two different time-reversal symmetry-protected topological phases [16][17][18]. We demonstrate how these two phases can be distinguished from each other using the projective composition rule of time-reversal twists induced by the inserted time-reversal fluxes.…”

Section: Introductionmentioning

confidence: 99%

Towards Gauging Time-Reversal Symmetry: A Tensor Network Approach

Xie

Vishwanath

2015

Phys. Rev. X

View full text Add to dashboard Cite

It is well known that unitary symmetries can be "gauged," i.e., defined to act in a local way, which leads to a corresponding gauge field. Gauging, for example, the charge-conservation symmetry leads to electromagnetic gauge fields. It is an open question whether an analogous process is possible for time reversal which is an antiunitary symmetry. Here, we discuss a route to gauging time-reversal symmetry that applies to gapped quantum ground states that admit a tensor network representation. The tensor network representation of quantum states provides a notion of locality for the wave function coefficient and hence a notion of locality for the action of complex conjugation in antiunitary symmetries. Based on that, we show how time reversal can be applied locally and also describe time-reversal symmetry twists that act as gauge fluxes through nontrivial loops in the system. As with unitary symmetries, gauging time reversal provides useful access to the physical properties of the system. We show how topological invariants of certain timereversal symmetric topological phases in D ¼ 1, 2 are readily extracted using these ideas.

show abstract

“…This non-trivial property is protected by symmetry, because once the symmetry is removed, the SPT phases can be smoothly connected to the trivial phase without phase transitions. 3 The well known Haldane phase 4 is an example of SPT phase in 1-dimension (1D). Topological insulators [5][6][7][8][9][10] are examples of SPT phases in higher dimensions.…”

Section: Introductionmentioning

confidence: 99%

Symmetry-protected topological phases in spin ladders with two-body interactions

et al. 2012

View full text Add to dashboard Cite

Spin-1/2 two-legged ladders respecting inter-leg exchange symmetry σ and spin rotation symmetry D2 have new symmetry protected topological (SPT) phases which are different from the Haldane phase. Three of the new SPT phases are tx, ty, tz, which all have symmetry protected two-fold degenerate edge states on each end of an open chain. However, the edge states in different phases have different response to magnetic field. For example, the edge states in the tz phase will be split by the magnetic field along the z-direction, but not by the fields in the x-and y-directions. We give the Hamiltonian that realizes each SPT phase and demonstrate a proof-of-principle quantum simulation scheme for Hamiltonians of the t0 and tz phases based on coupled-QED-cavity ladder.

show abstract

Entanglement spectrum of a topological phase in one dimension

Cited by 1,226 publications

References 37 publications

Competing Abelian and non-Abelian topological orders inν=1/3+1/3quantum Hall bilayers

Competing Abelian and non-Abelian topological orders inν=1/3+1/3quantum Hall bilayers

Towards Gauging Time-Reversal Symmetry: A Tensor Network Approach

Symmetry-protected topological phases in spin ladders with two-body interactions

Contact Info

Product

Resources

About