@article {bulmash_absolute_2020,
title = {Absolute anomalies in (2+1){D} symmetry-enriched topological states and exact (3+1){D} constructions},
journal = {Phys. Rev. Res.},
volume = {2},
number = {4},
year = {2020},
note = {Place: ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA Publisher: AMER PHYSICAL SOC Type: Article},
month = {oct},
abstract = {Certain patterns of symmetry fractionalization in (2+1)-dimensional [(2+1)D] topologically ordered phases of matter can be anomalous, which means that they possess an obstruction to being realized in purely (2+1)D. In this paper we demonstrate how to compute the anomaly for symmetry-enriched topological states of bosons in complete generality. We demonstrate how, given any unitary modular tensor category (UMTC) and symmetry fractionalization class for a global symmetry group G, one can define a (3+1)-dimensional [(3+1)D] topologically invariant path integral in terms of a state sum for a G-symmetry-protected topological (SPT) state. We present an exactly solvable Hamiltonian for the system and demonstrate explicitly a (2+1)D G-symmetric surface termination that hosts deconfined anyon excitations described by the given UMTC and symmetry fractionalization class. We present concrete algorithms that can be used to compute anomaly indicators in general. Our approach applies to general symmetry groups, including anyon-permuting and antiunitary symmetries. In addition to providing a general way to compute the anomaly, our result also shows, by explicit construction, that every symmetry fractionalization class for any UMTC can be realized at the surface of a (3+1)D SPT state. As a by-product, this construction also provides a way of explicitly seeing how the algebraic data that defines symmetry fractionalization in general arises in the context of exactly solvable models. In the case of unitary orientation-preserving symmetries, our results can also be viewed as providing a method to compute the H-4(G, U(1)) obstruction that arises in the theory of G-crossed braided tensor categories, for which no general method has been presented to date.},
doi = {10.1103/PhysRevResearch.2.043033},
author = {Bulmash, Daniel and Barkeshli, Maissam}
}
@article {aasen_topological_2020,
title = {Topological defect networks for fractons of all types},
journal = {Phys. Rev. Res.},
volume = {2},
number = {4},
year = {2020},
note = {Place: ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA Publisher: AMER PHYSICAL SOC Type: Article},
abstract = {Fracton phases exhibit striking behavior which appears to render them beyond the standard topological quantum field theory (TQFT) paradigm for classifying gapped quantum matter. Here, we explore fracton phases from the perspective of defect TQFTs and show that topological defect networks-networks of topological defects embedded in stratified 3+1-dimensional (3+1D) TQFTs-provide a unified framework for describing various types of gapped fracton phases. In this picture, the subdimensional excitations characteristic of fractonic matter are a consequence of mobility restrictions imposed by the defect network. We conjecture that all gapped phases, including fracton phases, admit a topological defect network description and support this claim by explicitly providing such a construction for many well-known fracton models, including the X-cube and Haah{\textquoteright}s B code. To highlight the generality of our framework, we also provide a defect network construction of a fracton phase hosting non-Abelian fractons. As a byproduct of this construction, we obtain a generalized membrane-net description for fractonic ground states as well as an argument that our conjecture implies no topological fracton phases exist in 2+1-dimensional gapped systems. Our paper also sheds light on techniques for constructing higher-order gapped boundaries of 3+1D TQFTs.},
doi = {10.1103/PhysRevResearch.2.043165},
author = {Aasen, David and Bulmash, Daniel and Prem, Abhinav and Slagle, Kevin and Williamson, Dominic J.}
}
@article {ISI:000461964300002,
title = {Braiding and gapped boundaries in fracton topological phases},
journal = {Phys. Rev. B},
volume = {99},
number = {12},
year = {2019},
month = {MAR 19},
pages = {125132},
publisher = {AMER PHYSICAL SOC},
type = {Article},
abstract = {We study gapped boundaries of Abelian type-I fracton systems in three spatial dimensions. Using the X-cube model as our motivating example, we give a conjecture, with partial proof, of the conditions for a boundary to be gapped. In order to state our conjecture, we use a precise definition of fracton braiding and show that bulk braiding of fractons has several features that make it insufficient to classify gapped boundaries. Most notable among these is that bulk braiding is sensitive to geometry and is {\textquoteleft}{\textquoteleft}nonreciprocal{{\textquoteright}{\textquoteright}}; that is, braiding an excitation a around b need not yield the same phase as braiding b around a. Instead, we define fractonic {\textquoteleft}{\textquoteleft}boundary braiding,{{\textquoteright}{\textquoteright}} which resolves these difficulties in the presence of a boundary. We then conjecture that a boundary of an Abelian fracton system is gapped if and only if a {\textquoteleft}{\textquoteleft}boundary Lagrangian subgroup{{\textquoteright}{\textquoteright}} of excitations is condensed at the boundary; this is a generalization of the condition for a gapped boundary in two spatial dimensions, but it relies on boundary braiding instead of bulk braiding. We also discuss the distinctness of gapped boundaries and transitions between different topological orders on gapped boundaries.},
issn = {2469-9950},
doi = {10.1103/PhysRevB.99.125132},
author = {Bulmash, Daniel and Iadecola, Thomas}
}
@article { ISI:000493516700001,
title = {Gauging fractons: Immobile non-Abelian quasiparticles, fractals, and position-dependent degeneracies},
journal = {Phys. Rev. B},
volume = {100},
number = {15},
year = {2019},
month = {OCT 29},
pages = {155146},
publisher = {AMER PHYSICAL SOC},
type = {Article},
abstract = {The study of gapped quantum many-body systems in three spatial dimensions has uncovered the existence of quantum states hosting quasiparticles that are confined, not by energetics but by the structure of local operators, to move along lower dimensional submanifolds. These so-called {\textquoteleft}{\textquoteleft}fracton{{\textquoteright}{\textquoteright}} phases are beyond the usual topological quantum field theory description, and thus require new theoretical frameworks to describe them. Here we consider coupling fracton models to topological quantum field theories in (3 + 1) dimensions by starting with two copies of a known fracton model and gauging the Z(2) symmetry that exchanges the two copies. This yields a class of exactly solvable lattice models that we study in detail for the case of the X-cube model and Haah{\textquoteright}s cubic code. The resulting phases host finite-energy non-Abelian immobile quasiparticles with robust degeneracies that depend on their relative positions. The phases also host non-Abelian string excitations with robust degeneracies that depend on the string geometry. Applying the construction to Haah{\textquoteright}s cubic code in particular provides an exactly solvable model with finite energy yet immobile non-Abelian quasiparticles that can only be created at the corners of operators with fractal support.},
issn = {2469-9950},
doi = {10.1103/PhysRevB.100.155146},
author = {Bulmash, Daniel and Barkeshli, Maissam}
}
@article {ISI:000457732400002,
title = {Wiedemann-Franz law and Fermi liquids},
journal = {Phys. Rev. B},
volume = {99},
number = {8},
year = {2019},
month = {FEB 4},
pages = {085104},
publisher = {AMER PHYSICAL SOC},
type = {Article},
abstract = {We consider in depth the applicability of the Wiedemann-Franz (WF) law, namely that the electronic thermal conductivity (K) is proportional to the product of the absolute temperature (T) and the electrical conductivity (a) in a metal with the constant of proportionality, the so-called Lorenz number L-0, being a materials-independent universal constant in all systems obeying the Fermi liquid (FL) paradigm. It has been often stated that the validity (invalidity) of the WF law is the hallmark of an FL {[}non-Fermi liquid (NFL)]. We consider, both in two (2D) and three (3D) dimensions, a system of conduction electrons at a finite temperature T coupled to a bath of acoustic phonons and quenched impurities, ignoring effects of electron-electron interactions. We find that the WF law is violated arbitrarily strongly with the effective Lorenz number vanishing at low temperatures as long as phonon scattering is stronger than impurity scattering. This happens both in 2D and in 3D for T < T-BG, where T-BG is the Bloch-Griineisen temperature of the system. In the absence of phonon scattering (or equivalently, when impurity scattering is much stronger than the phonon scattering), however, the WF law is restored at low temperatures even if the impurity scattering is mostly small angle forward scattering. Thus, strictly at T = 0 the WF law is always valid in a FL in the presence of infinitesimal impurity scattering. For strong phonon scattering, the WF law is restored for T > T-BG (or the Debye temperature T-D, whichever is lower) as in usual metals. At very high temperatures, thermal smearing of the Fermi surface causes the effective Lorenz number to go below L-0, manifesting a quantitative deviation from the WF law. Our paper establishes definitively that the uncritical association of an NFL behavior with the failure of the WF law is incorrect.},
issn = {2469-9950},
doi = {10.1103/PhysRevB.99.085104},
author = {Lavasani, Ali and Bulmash, Daniel and S. Das Sarma}
}
@article { ISI:000434628400002,
title = {Higgs mechanism in higher-rank symmetric U(1) gauge theories},
journal = {PHYSICAL REVIEW B},
volume = {97},
number = {23},
year = {2018},
month = {JUN 8},
pages = {235112},
issn = {2469-9950},
doi = {10.1103/PhysRevB.97.235112},
author = {Bulmash, Daniel and Barkeshli, Maissam}
}