TY - JOUR T1 - Kramers' degeneracy for open systems in thermal equilibrium JF - Phys. Rev. B Y1 - 2022 A1 - Simon Lieu A1 - Max McGinley A1 - Oles Shtanko A1 - Nigel R. Cooper A1 - Alexey V. Gorshkov VL - 105 U4 - L121104 UR - https://arxiv.org/abs/2105.02888 CP - 12 U5 - https://doi.org/10.1103/PhysRevB.105.L121104 ER - TY - JOUR T1 - Keyring models: an approach to steerability JF - Journal of Mathematical Physics Y1 - 2018 A1 - Carl Miller A1 - Roger Colbeck A1 - Yaoyun Shi AB -

If a measurement is made on one half of a bipartite system then, conditioned on the outcome, the other half has a new reduced state. If these reduced states defy classical explanation — that is, if shared randomness cannot produce these reduced states for all possible measurements — the bipartite state is said to be steerable. Determining which states are steerable is a challenging problem even for low dimensions. In the case of two-qubit systems a criterion is known for T-states (that is, those with maximally mixed marginals) under projective measurements. In the current work we introduce the concept of keyring models — a special class of local hidden state model. When the measurements made correspond to real projectors, these allow us to study steerability beyond T-states. Using keyring models, we completely solve the steering problem for real projective measurements when the state arises from mixing a pure two-qubit state with uniform noise. We also give a partial solution in the case when the uniform noise is replaced by independent depolarizing channels. Our results imply that Werner states, which are a special case of the previous states, are unsteerable under real projective measurements if and only if their efficiency is at most 2/π.

VL - 59 U4 - 022103 UR - http://aip.scitation.org/doi/full/10.1063/1.5006199 U5 - 10.1063/1.5006199 ER - TY - JOUR T1 - Kaleidoscope of quantum phases in a long-range interacting spin-1 chain JF - Physical Review B Y1 - 2016 A1 - Zhe-Xuan Gong A1 - Mohammad F. Maghrebi A1 - Anzi Hu A1 - Michael Foss-Feig A1 - Philip Richerme A1 - Christopher Monroe A1 - Alexey V. Gorshkov AB - Motivated by recent trapped-ion quantum simulation experiments, we carry out a comprehensive study of the phase diagram of a spin-1 chain with XXZ-type interactions that decay as 1/rα, using a combination of finite and infinite-size DMRG calculations, spin-wave analysis, and field theory. In the absence of long-range interactions, varying the spin-coupling anisotropy leads to four distinct phases: a ferromagnetic Ising phase, a disordered XY phase, a topological Haldane phase, and an antiferromagnetic Ising phase. If long-range interactions are antiferromagnetic and thus frustrated, we find primarily a quantitative change of the phase boundaries. On the other hand, ferromagnetic (non-frustrated) long-range interactions qualitatively impact the entire phase diagram. Importantly, for α≲3, long-range interactions destroy the Haldane phase, break the conformal symmetry of the XY phase, give rise to a new phase that spontaneously breaks a U(1) continuous symmetry, and introduce an exotic tricritical point with no direct parallel in short-range interacting spin chains. We show that the main signatures of all five phases found could be observed experimentally in the near future. VL - 93 U4 - 205115 UR - http://arxiv.org/abs/1510.02108 CP - 20 U5 - http://dx.doi.org/10.1103/PhysRevB.93.205115 ER - TY - JOUR T1 - Kitaev chains with long-range pairing JF - Physical Review Letters Y1 - 2014 A1 - Davide Vodola A1 - Luca Lepori A1 - Elisa Ercolessi A1 - Alexey V. Gorshkov A1 - Guido Pupillo AB - We propose and analyze a generalization of the Kitaev chain for fermions with long-range $p$-wave pairing, which decays with distance as a power-law with exponent $\alpha$. Using the integrability of the model, we demonstrate the existence of two types of gapped regimes, where correlation functions decay exponentially at short range and algebraically at long range ($\alpha > 1$) or purely algebraically ($\alpha < 1$). Most interestingly, along the critical lines, long-range pairing is found to break conformal symmetry for sufficiently small $\alpha$. This is accompanied by a violation of the area law for the entanglement entropy in large parts of the phase diagram in the presence of a gap, and can be detected via the dynamics of entanglement following a quench. Some of these features may be relevant for current experiments with cold atomic ions. VL - 113 UR - http://arxiv.org/abs/1405.5440v2 CP - 15 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.113.156402 ER - TY - JOUR T1 - Kitaev honeycomb and other exotic spin models with polar molecules JF - Molecular Physics Y1 - 2013 A1 - Alexey V. Gorshkov A1 - Kaden R. A. Hazzard A1 - Ana Maria Rey AB - We show that ultracold polar molecules pinned in an optical lattice can be used to access a variety of exotic spin models, including the Kitaev honeycomb model. Treating each molecule as a rigid rotor, we use DC electric and microwave fields to define superpositions of rotational levels as effective spin degrees of freedom, while dipole-dipole interactions give rise to interactions between the spins. In particular, we show that, with sufficient microwave control, the interaction between two spins can be written as a sum of five independently controllable Hamiltonian terms proportional to the five rank-2 spherical harmonics Y_{2,q}(theta,phi), where (theta,phi) are the spherical coordinates of the vector connecting the two molecules. To demonstrate the potential of this approach beyond the simplest examples studied in [S. R. Manmana et al., arXiv:1210.5518v2], we focus on the realization of the Kitaev honeycomb model, which can support exotic non-Abelian anyonic excitations. We also discuss the possibility of generating spin Hamiltonians with arbitrary spin S, including those exhibiting SU(N=2S+1) symmetry. VL - 111 U4 - 1908 - 1916 UR - http://arxiv.org/abs/1301.5636v1 CP - 12-13 J1 - Molecular Physics U5 - 10.1080/00268976.2013.800604 ER -