@article { WOS:000688493300002,
title = {Z(2) topological order and first-order quantum phase transitions in systems with combinatorial gauge symmetry},
journal = {Phys. Rev. B},
volume = {104},
number = {8},
year = {2021},
month = {AUG 24},
publisher = {AMER PHYSICAL SOC},
type = {Article},
abstract = {We study a generalization of the two-dimensional transverse-field Ising model, combining both ferromagnetic and antiferromagnetic two-body interactions, that hosts exact global and local Z(2) gauge symmetries. Using exact diagonalization and stochastic series expansion quantum Monte Carlo methods, we confirm the existence of the topological phase in line with previous theoretical predictions. Our simulation results show that the transition between the confined topological phase and the deconfined paramagnetic phase is of first order, in contrast to the conventional Z(2) lattice gauge model in which the transition maps onto that of the standard Ising model and is continuous. We further generalize the model by replacing the transverse field on the gauge spins with a ferromagnetic XX interaction while keeping the local gauge symmetry intact. We find that the Z(2) topological phase remains stable, while the paramagnetic phase is replaced by a ferromagnetic phase. The topological-ferromagnetic quantum phase transition is also of first order. For both models, we discuss the low-energy spinon and vison excitations of the topological phase and their avoided level crossings associated with the first-order quantum phase transitions.},
issn = {2469-9950},
doi = {10.1103/PhysRevB.104.085145},
author = {Wu, Kai-Hsin and Yang, Zhi-Cheng and Green, Dmitry and Sandvik, Anders W. and Chamon, Claudio}
}
@article { WOS:000685127300001,
title = {Z(3) Quantum Double in a Superconducting Wire Array},
journal = {PRX Quantum},
volume = {2},
number = {3},
year = {2021},
month = {AUG 13},
publisher = {AMER PHYSICAL SOC},
type = {Article},
abstract = {We show that a Z(3) quantum double can be realized in an array of superconducting wires coupled via Josephson junctions. With a suitably chosen magnetic flux threading the system, the interwire Josephson couplings take the form of a complex Hadamard matrix, which possesses combinatorial gauge symmetry-a local Z(3) symmetry involving permutations and shifts by +/- 2 pi/3 of the superconducting phases. The sign of the star potential resulting from the Josephson energy is inverted in this physical realization, leading to a massive degeneracy in the nonzero flux sectors. A dimerization pattern encoded in the capacitances of the array lifts up these degeneracies, resulting in a Z(3) topologically ordered state. Moreover, this dimerization pattern leads to a larger effective vison gap as compared to the canonical case with the usual (uninverted) star term. We further show that our model maps to a quantum three-state Potts model under a duality transformation. We argue, using a combination of bosonization and mean field theory, that altering the dimerization pattern of the capacitances leads to a transition from the Z(3) topological phase into a quantum XY-ordered phase. Our work highlights that combinatorial gauge symmetry can serve as a design principle to build quantum double models using systems with realistic interactions.},
doi = {10.1103/PRXQuantum.2.030327},
author = {Yang, Zhi-Cheng and Green, Dmitry and Yu, Hongji and Chamon, Claudio}
}
@article { WOS:000649079900009,
title = {Zeroth law in quantum thermodynamics at strong coupling: In equilibrium, not at equal temperature},
journal = {Phys. Rev. D},
volume = {103},
number = {8},
year = {2021},
month = {APR 13},
publisher = {AMER PHYSICAL SOC},
type = {Article},
abstract = {The zeroth law of thermodynamics involves a transitivity relation (pairwise between three objects) expressed either in terms of {\textquoteleft}{\textquoteleft}equal temperature{{\textquoteright}{\textquoteright}} (ET), or {\textquoteleft}{\textquoteleft}in equilibrium{{\textquoteright}{\textquoteright}} (EQ) conditions. In conventional thermodynamics conditional on vanishingly weak system-bath coupling these two conditions are commonly regarded as equivalent. In this work we show that for thermodynamics at strong coupling they are inequivalent: namely, two systems can he in equilibrium and yet have different effective temperatures. A recent result {[}J.-T. Hsiang and B. L. Hu, Phys. Rev. D 103, 065001 (2021) for Gaussian quantum systems shows that an effective temperature r can be defined at all times during a system{\textquoteright}s nonequilibrium evolution, but because of the inclusion of interaction energy, after equilibration the system{\textquoteright}s T{*} is slightly higher than the bath temperature T-B, with the deviation depending on the coupling. A second object coupled with a different strength with an identical bath at temperature T-B will not have the same equilibrated temperature as the first object. Thus ET not equal EQ for strong coupling thermodynamics. We then investigate the conditions for dynamical equilibration for two objects 1 and 2 strongly coupled with a common bath B, each with a different equilibrated effective temperature. We show this is possible, and prove the existence of a generalized fluctuation-dissipation relation under this configuration. This affirms that in equilibrium is a valid and perhaps more fundamental notion which the zeroth law for quantum thermodynamics at strong coupling should be based on. Only when the system-bath coupling becomes vanishingly weak that {\textquoteleft}{\textquoteleft}temperature{{\textquoteright}{\textquoteright}} appearing in thermodynamic relations becomes universally defined and makes better physical sense.},
issn = {2470-0010},
doi = {10.1103/PhysRevD.103.085004},
author = {Hsiang, Jen-Tsung and Hu, Bei-Lok}
}
@article {balram_zn_2020,
title = {Z(n) superconductivity of composite bosons and the 7/3 fractional quantum {Hall} effect},
journal = {Phys. Rev. Res.},
volume = {2},
number = {1},
year = {2020},
note = {Place: ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA Publisher: AMER PHYSICAL SOC Type: Article},
month = {mar},
abstract = {The topological p-wave pairing of composite fermions, believed to be responsible for the 5/2 fractional quantum Hall effect (FQHE), has generated much exciting physics. Motivated by the parton theory of the FQHE, we consider the possibility of a new kind of emergent {\textquotedblleft}superconductivity{\textquotedblright} in the 1/3 FQHE, which involves condensation of clusters of n composite bosons. From a microscopic perspective, the state is described by the n (n) over bar 111 parton wave function P-LLL Phi(n)Phi(n)*Phi(3)(1), where Phi(n) is the wave function of the integer quantum Hall state with n filled Landau levels and P-LLL is the lowest-Landau-level projection operator. It represents a Z(n) superconductor of composite bosons, because the factor Phi(3)(1) similar to Pi(j{\textless}k) (z(j) - z(k))(3), where z(j) = x(j) - iy(j) is the coordinate of the jth electron, binds three vortices to electrons to convert them into composite bosons, which then condense into the Z(n) superconducting state vertical bar Phi(n)vertical bar(2). From a field theoretical perspective, this state can be understood by starting with the usual Laughlin theory and gauging a Z(n) subgroup of the U(1) charge conservation symmetry. We find from detailed quantitative calculations that the 2{\textless}(2)over bar{\textgreater}111 and 3 (3) over bar 111 states are at least as plausible as the Laughlin wave function for the exact Coulomb ground state at filling nu = 7/3, suggesting that this physics is possibly relevant for the 7/3 FQHE. The Z(n) order leads to several observable consequences, including quasiparticles with fractionally quantized charges of magnitude e/(3n) and the existence of multiple neutral collective modes. It is interesting that the FQHE may be a promising venue for the realization of exotic Z(n) superconductivity.},
doi = {10.1103/PhysRevResearch.2.013349},
author = {Balram, Ajit C. and Jain, J. K. and Barkeshli, Maissam}
}
@article { ISI:000415687200020,
title = {Z(3) Parafermionic Zero Modes without Andreev Backscattering from the 2/3 Fractional Quantum Hall State},
journal = {PHYSICAL REVIEW LETTERS},
volume = {119},
number = {21},
year = {2017},
month = {NOV 20},
issn = {0031-9007},
doi = {10.1103/PhysRevLett.119.217701},
author = {Alavirad, Yahya and Clarke, David and Nag, Amit and Sau, Jay D.}
}
@article { ISI:000337348300008,
title = {Z(2) index for gapless fermionic modes in the vortex core of three-dimensional paired Dirac fermions},
journal = {PHYSICAL REVIEW B},
volume = {89},
number = {14},
year = {2014},
month = {APR 14},
issn = {1098-0121},
doi = {10.1103/PhysRevB.89.144507},
author = {Roy, Bitan and Goswami, Pallab}
}
@article { ISI:000338043100001,
title = {Zero Modes and Global Antiferromagnetism in Strained Graphene},
journal = {PHYSICAL REVIEW X},
volume = {4},
number = {2},
year = {2014},
month = {MAY 30},
issn = {2160-3308},
doi = {10.1103/PhysRevX.4.021042},
author = {Roy, Bitan and Assaad, Fakher F. and Herbut, Igor F.}
}
@article {ISI:000312364700008,
title = {Zero-bias conductance peak in Majorana wires made of semiconductor/superconductor hybrid structures},
journal = {Phys. Rev. B},
volume = {86},
number = {22},
year = {2012},
month = {dec},
pages = {224511},
issn = {1098-0121},
doi = {10.1103/PhysRevB.86.224511},
author = {Chien-Hung Lin and Jay D Sau and S. Das Sarma}
}