540 citations · 4.8k across the 94 of their papers we have counts for
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Crystalline topological invariants in quantum many-body systems
Naren Manjunath, Maissam Barkeshli
Crystalline symmetries give rise to topological invariants that can distinguish quantum phases of matter. Understanding these in strongly interacting systems is an ongoing research…
Invariants for (2+1)D bosonic crystalline topological insulators for all 17 wallpaper groups
Vladimir Calvera, Naren Manjunath, Maissam Barkeshli
We study bosonic symmetry-protected topological (SPT) phases in (2+1) dimensions with symmetry , where is a general wallpaper group…
Electric polarization in Chern insulators: Unifying many-body and single-particle approaches
Yuxuan Zhang, Maissam Barkeshli
Recently, it has been established that Chern insulators possess an intrinsic two-dimensional electric polarization, despite having gapless edge states and non-localizable Wannier o…
Disclinations, dislocations, and emanant flux at Dirac criticality
Maissam Barkeshli, Christopher Fechisin, Zohar Komargodski +1
What happens when fermions hop on a lattice with crystalline defects? The answer depends on topological quantum numbers which specify the action of lattice rotations and translatio…
Soft symmetries of topological orders
Ryohei Kobayashi, Maissam Barkeshli
(2+1)D topological orders possess emergent symmetries given by a group , which consists of the braided tensor autoequivalences of the modular tensor catego…
Fractionally Quantized Electric Polarization and Discrete Shift of Crystalline Fractional Chern Insulators
Yuxuan Zhang, Maissam Barkeshli
Fractional Chern insulators (FCI) with crystalline symmetry possess topological invariants that fundamentally have no analog in continuum fractional quantum Hall (FQH) states. Here…
Electric polarization and discrete shift from boundary and corner charge in crystalline Chern insulators
Yuxuan Zhang, Maissam Barkeshli
Recently, it has been shown how topological phases of matter with crystalline symmetry and charge conservation can be partially characterized by a set of many-body invariant…
Crystalline invariants of fractional Chern insulators
Ryohei Kobayashi, Yuxuan Zhang, Naren Manjunath +1
In the presence of crystalline symmetry, topologically ordered states can acquire a host of symmetry-protected invariants. These determine the patterns of crystalline symmetry frac…
(2+1)D topological phases with RT symmetry: many-body invariant, classification, and higher order edge modes
Ryohei Kobayashi, Yuxuan Zhang, Yan-Qi Wang +1
It is common in condensed matter systems for reflection () and time-reversal () symmetry to both be broken while the combination is preserved. In this paper we study inv…
Higher-group symmetry of (3+1)D fermionic gauge theory: logical CCZ, CS, and T gates from higher symmetry
Maissam Barkeshli, Po-Shen Hsin, Ryohei Kobayashi
It has recently been understood that the complete global symmetry of finite group topological gauge theories contains the structure of a higher-group. Here we study the higher-grou…
Characterization and classification of interacting (2+1)D topological crystalline insulators with orientation-preserving wallpaper groups
Naren Manjunath, Vladimir Calvera, Maissam Barkeshli
While free fermion topological crystalline insulators have been largely classified, the analogous problem in the strongly interacting case has been only partially solved. In this p…
Complete crystalline topological invariants from partial rotations in (2+1)D invertible fermionic states and Hofstadter's butterfly
Yuxuan Zhang, Naren Manjunath, Ryohei Kobayashi +1
The theory of topological phases of matter predicts invariants protected only by crystalline symmetry, yet it has been unclear how to extract these from microscopic calculations in…
Higher-group symmetry in finite gauge theory and stabilizer codes
Maissam Barkeshli, Yu-An Chen, Po-Shen Hsin +1
A large class of gapped phases of matter can be described by topological finite group gauge theories. In this paper we show how such gauge theories possess a higher-group global sy…
Quantized charge polarization as a many-body invariant in (2+1)D crystalline topological states and Hofstadter butterflies
Yuxuan Zhang, Naren Manjunath, Gautam Nambiar +1
We show how to define a quantized many-body charge polarization for (2+1)D topological phases of matter, even in the presence of non-zero Chern number and magne…
Extracting Wilson loop operators and fractional statistics from a single bulk ground state
Ze-Pei Cian, Mohammad Hafezi, Maissam Barkeshli
An essential aspect of topological phases of matter is the existence of Wilson loop operators that keep the ground state subspace invariant. Here we present and implement an \it un…
Non-perturbative constraints from symmetry and chirality on Majorana zero modes and defect quantum numbers in (2+1)D
Naren Manjunath, Vladimir Calvera, Maissam Barkeshli
In (1+1)D topological phases, unpaired Majorana zero modes (MZMs) can arise only if the internal symmetry group of the ground state splits as $G_f = G_b \times \mathbb{Z}_2^f…
Codimension-2 defects and higher symmetries in (3+1)D topological phases
Maissam Barkeshli, Yu-An Chen, Sheng-Jie Huang +3
(3+1)D topological phases of matter can host a broad class of non-trivial topological defects of codimension-1, 2, and 3, of which the well-known point charges and flux loops are s…
Fractional disclination charge and discrete shift in the Hofstadter butterfly
Yuxuan Zhang, Naren Manjunath, Gautam Nambiar +1
In the presence of crystalline symmetries, topological phases of matter acquire a host of invariants leading to non-trivial quantized responses. Here we study a particular invarian…
(3+1)D path integral state sums on curved U(1) bundles and U(1) anomalies of (2+1)D topological phases
Ryohei Kobayashi, Maissam Barkeshli
Given the algebraic data characterizing any (2+1)D bosonic or fermionic topological order with a global symmetry group , we construct a (3+1)D topologi…
Classification of (2+1)D invertible fermionic topological phases with symmetry
Maissam Barkeshli, Yu-An Chen, Po-Shen Hsin +1
We provide a classification of invertible topological phases of interacting fermions with symmetry in two spatial dimensions for general fermionic symmetry groups and general…
Anomaly cascade in (2+1)D fermionic topological phases
Daniel Bulmash, Maissam Barkeshli
We develop a theory of anomalies of fermionic topological phases of matter in (2+1)D with a general fermionic symmetry group . In general, can be a non-trivial central e…
Fermionic symmetry fractionalization in (2+1)D
Daniel Bulmash, Maissam Barkeshli
We develop a systematic theory of symmetry fractionalization for fermionic topological phases of matter in (2+1)D with a general fermionic symmetry group . In general is…
Anomalies in (2+1)D fermionic topological phases and (3+1)D path integral state sums for fermionic SPTs
Sri Tata, Ryohei Kobayashi, Daniel Bulmash +1
Given a (2+1)D fermionic topological order and a symmetry fractionalization class for a global symmetry group , we show how to construct a (3+1)D topologically invariant path in…
Classification of fractional quantum Hall states with spatial symmetries
Naren Manjunath, Maissam Barkeshli
Fractional quantum Hall (FQH) states are examples of symmetry-enriched topological states (SETs): in addition to the intrinsic topological order, which is robust to symmetry breaki…