Long coherence times for edge spins

Kemp, Jack; Yao, Norman Y.; Laumann, Chris R.; Fendley, Paul

doi:10.1088/1742-5468/aa73f0

Cited by 99 publications

(172 citation statements)

References 40 publications

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“…of thermalization. As we shall see, the effect of SLIOMs is strongest near the boundary, where they lead to infinitely long coherence times, in complete analogy with the case of strong zero modes [53][54][55][56][57][58]. In the bulk, we find that coherence times are finite in the thermodynamic limit, despite the presence of infinitely many conservation laws.…”

Section: Bulk Vs Boundary Slioms and Their Relationship To Thermalsupporting

confidence: 59%

Statistical localization: From strong fragmentation to strong edge modes

et al. 2020

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Certain disorder-free Hamiltonians can be non-ergodic due to a strong fragmentation of the Hilbert space into disconnected sectors. Here, we characterize such systems by introducing the notion of 'statistically localized integrals of motion' (SLIOM), whose eigenvalues label the connected components of the Hilbert space. SLIOMs are not spatially localized in the operator sense, but appear localized to sub-extensive regions when their expectation value is taken in typical states with a finite density of particles. We illustrate this general concept on several Hamiltonians, both with and without dipole conservation. Furthermore, we demonstrate that there exist perturbations which destroy these integrals of motion in the bulk of the system, while keeping them on the boundary. This results in statistically localized strong zero modes, leading to infinitely long-lived edge magnetizations along with a thermalizing bulk, constituting the first example of such strong edge modes in a non-integrable model. We also show that in a particular example, these edge modes lead to the appearance of topological string order in a certain subset of highly excited eigenstates. Some of our suggested models can be realized in Rydberg quantum simulators.CONTENTS * These authors contributed equally to this work.

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Section: Bulk Vs Boundary Slioms and Their Relationship To Thermalsupporting

confidence: 59%

Statistical localization: From strong fragmentation to strong edge modes

et al. 2020

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“…We presented an analytical argument that excludes a strong zero mode for a large part of the topological phase. To address the remaining region, we calculated the time dependence of the edge magnetization 48 . In the remaining region, these results rule out a strong zero mode in the case that either h or |U | is large.…”

Section: Discussionmentioning

confidence: 99%

Study of the phase diagram of the Kitaev-Hubbard chain

Mahyaeh

Ardonne

2020

Phys. Rev. B

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We present a detailed study of the phase diagram of the Kitaev-Hubbard chain, that is the Kitaev chain in the presence of a nearest-neighbour density-density interaction, using both analytical techniques as well as DMRG. In the case of a moderate attractive interaction, the model has the same phases as the non-interacting chain, a trivial and a topological phase. For repulsive interactions, the phase diagram is more interesting. Apart from the previously observed topological, incommensurate and charge density wave phases, we identify the 'excited state charge density wave' phase. In this phase, the ground state resembles an excited state of an ordinary charge density phase, but is lower in energy due to the frustrated nature of the model. We find that the dynamical critical exponent takes the value z 1.8. Interestingly, this phase only appears for even system sizes, and is sensitive to the chemical potential on the edges of the chain. For the topological phase, we present an argument that excludes the presence of a strong zero mode for a large part of the topological phase. For the remaining region, we study the time dependence of the edge magnetization (using the bosonic incarnation of the model). These results further expand the region where a strong zero mode does not occur. arXiv:1911.03156v2 [cond-mat.str-el]

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“…This gives another hint of the fact that when θ is such that the total domain-wall angle is not conserved, the zero mode operator cannot be constructed, as the presence of Q 0 H 0 will induce divergences at resonant points that cannot be removed. In particular this accounts for the divergences witnessed in the expansion of the zero mode in [8,14,26].…”

Section: General Form Of the Solutionmentioning

confidence: 89%

“…Despite this, the norm of ψ may still diverge if the limit L → ∞ is taken at fixed f , because the coefficient in front of the f L term may grow quickly with L, similarly to what happens in [14] for spin chains. We will consider this further in Section 8.…”

Section: Parafermionic Zero Modesmentioning

confidence: 98%

Constructing edge zero modes through domain wall angle conservation

Pellegrino

Kells

Moran

et al. 2020

J. Phys. A: Math. Theor.

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We investigate the existence, normalization and explicit construction of edge zero modes in topologically ordered spin chains. In particular we give a detailed treatment of zero modes in a Z 3 generalization of the Ising/Kitaev chain, which can also be described in terms of parafermions. We analyze when it is possible to iteratively construct strong zero modes, working completely in the spin picture. An important role is played by the so called total domain wall angle, a symmetry which appears in all models with strong zero modes that we are aware of. We show that preservation of this symmetry guarantees locality of the iterative construction, that is, it imposes locality conditions on the successive terms appearing in the zero mode's perturbative expansion. The method outlined here summarizes and generalizes some of the existing techniques used to construct zero modes in spin chains and sheds light on some surprising common features of all these types of methods. We conjecture a general algorithm for the perturbative construction of zero mode operators and test this on a variety of models, to the highest order we can manage. We also present analytical formulas for the zero modes which apply to all models investigated, but which feature a number of model dependent coefficients.

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Long coherence times for edge spins

Cited by 99 publications

References 40 publications

Statistical localization: From strong fragmentation to strong edge modes

Statistical localization: From strong fragmentation to strong edge modes

Study of the phase diagram of the Kitaev-Hubbard chain

Constructing edge zero modes through domain wall angle conservation

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