Interacting symmetry-protected topological phases out of equilibrium

McGinley, Max; Cooper, N. R.

doi:10.1103/physrevresearch.1.033204

Cited by 24 publications

(17 citation statements)

References 67 publications

(148 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…When the system in question features a combination of unitary and antiunitary symmetries, one can determine whether the coherence will remain protected by consulting the classification tables in Refs. [23,24], which enumerate those phases that are stable once antiunitary symmetries are removed.…”

Section: Coherence Time Of Topological Bound Statesmentioning

confidence: 99%

“…Our newfound intuition suggests that if the SPT is protected by (anti-)unitary symmetries, then the topological bound state will (not) remain coherent upon coupling to an environment. More precisely, those phases that can be trivialized by explicitly breaking all antiunitary symmetries will exhibit decoherence; this particular class of SPTs has been classified in a different context [23,24].…”

mentioning

confidence: 99%

See 1 more Smart Citation

Fragility of time-reversal symmetry protected topological phases

McGinley

Cooper

2020

Nat. Phys.

Self Cite

View full text Add to dashboard Cite

The second law of thermodynamics points to the existence of an 'arrow of time', along which entropy only increases. This arises despite the time-reversal symmetry (TRS) of the microscopic laws of nature. Within quantum theory, TRS underpins many interesting phenomena, most notably topological insulators [1][2][3][4] and the Haldane phase of quantum magnets [5,6]. Here, we demonstrate that such TRS-protected effects are fundamentally unstable against coupling to an environment. Irrespective of the microscopic symmetries, interactions between a quantum system and its surroundings facilitate processes which would be forbidden by TRS in an isolated system. This leads not only to entanglement entropy production and the emergence of macroscopic irreversibility [7,8], but also to the demise of TRS-protected phenomena, including those associated with certain symmetry-protected topological phases. Our results highlight the enigmatic nature of TRS in quantum mechanics, and elucidate potential challenges in utilising topological systems for quantum technologies.Many isolated systems possess features that rely on symmetries of their Hamiltonian. Most strikingly, in many-body systems the presence of symmetries leads to new phases of matter, including symmetry-protected topological phases (SPTs) [9,10]. SPTs exhibit many remarkable features, such as the emergence of topological bound states (e.g. Majorana zero modes [11]), which have potential applications in quantum information processing [12,13].An important practical question, which we address in this Letter, is whether symmetry-protected phenomena such as these can persist in realistic scenarios where the system is weakly coupled to an environment. Previous studies of topology in open systems begin with an approximate equation of motion for the system (e.g. non-Hermitian Hamiltonian [14] or Lindblad master equation [15][16][17]). Instead, our starting point is the full systemenvironment Hamiltonian

show abstract

Section: Coherence Time Of Topological Bound Statesmentioning

confidence: 99%

mentioning

confidence: 99%

Fragility of time-reversal symmetry protected topological phases

McGinley

Cooper

2020

Nat. Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

“…To complete the comparison of S D to a topological invariant, it would be interesting to investigate the evolution of S D when the protecting symmetry is explicitly broken and the maximal entanglement of the edge state is no more set topologically, such as in the Rice-Mele model [79]. It would also be interesting to use entanglement topological invariants to characterize the real-time dynamics of other instances of topological insulators in the presence of a bath [66].…”

Section: Discussionmentioning

confidence: 99%

“…Thus, β i,r (t) = o(1/r) on all sites and for all times: although the range of H fic (t) increases with time, the Hamiltonian is short range. H i and H fic (t) are thus connected unitarily, continuously, locally and without closing the gap, as if by an adiabatic connection [64][65][66] (no extra hypothesis of adiabaticity was imposed in the reasoning). Therefore, unless the system experiences a dynamical phase transition, H i and H fic (t) are in the same topological phase relative to the PHS, and if one has robust edge states, so does the other.…”

Section: Invariance Of S D During Unitary Evolution: the Role Of Partmentioning

confidence: 99%

Topological entanglement properties of disconnected partitions in the Su-Schrieffer-Heeger model

et al. 2020

View full text Add to dashboard Cite

We study the disconnected entanglement entropy, S^\mathrm{D}SD, of the Su-Schrieffer-Heeger model. S^\mathrm{D}SD is a combination of both connected and disconnected bipartite entanglement entropies that removes all area and volume law contributions and is thus only sensitive to the non-local entanglement stored within the ground state manifold. Using analytical and numerical computations, we show that S^\mathrm{D}SD behaves like a topological invariant, i.e., it is quantized to either 00 or 2\log(2)2log(2) in the topologically trivial and non-trivial phases, respectively. These results also hold in the presence of symmetry-preserving disorder. At the second-order phase transition separating the two phases, S^\mathrm{D}SD displays a finite-size scaling behavior akin to those of conventional order parameters, that allows us to compute entanglement critical exponents. To corroborate the topological origin of the quantized values of S^\mathrm{D}SD, we show how the latter remain quantized after applying unitary time evolution in the form of a quantum quench, a characteristic feature of topological invariants associated with particle-hole symmetry.

show abstract

“…Introduction.-Classification of topological phases of matter is a central issue in modern condensed matter physics [1]. Particular recent interest is attracted by the classification of topological systems far from thermal equilibrium [2][3][4][5][6][7][8][9][10][11][12][13][14][15]. This tendency is largely driven by the remarkable experimental developments in atomic, molecular and optical physics, which have opened up unprecedented flexibility for controlling and probing quantum many-body dynamics [16][17][18][19][20][21].…”

mentioning

confidence: 99%

Classification of Matrix-Product Unitaries with Symmetries

et al. 2020

View full text Add to dashboard Cite

We prove that matrix-product unitaries with on-site unitary symmetries are completely classified by the (chiral) index and the cohomology class of the symmetry group G, provided that we can add trivial and symmetric ancillas with arbitrary on-site representations of G. If the representations in both system and ancillas are fixed to be the same, we can define symmetry-protected indices (SPIs) which quantify the imbalance in the transport associated to each group element and greatly refines the classification. These SPIs are stable against disorder and measurable in interferometric experiments. Our results lead to a systematic construction of two-dimensional Floquet symmetry-protected topological phases beyond the standard classification, and thus shed new light on understanding nonequilibrium phases of quantum matter.

show abstract

Interacting symmetry-protected topological phases out of equilibrium

Cited by 24 publications

References 67 publications

Fragility of time-reversal symmetry protected topological phases

Fragility of time-reversal symmetry protected topological phases

Topological entanglement properties of disconnected partitions in the Su-Schrieffer-Heeger model

Classification of Matrix-Product Unitaries with Symmetries

Contact Info

Product

Resources

About