Related papers: Reflection positivity and invertible topological p…
In this letter, we analyze the topological response of a fermionic model defined on the Lieb lattice in presence of an electromagnetic field. The tight-binding model is built in terms of three species of spinless fermions and supports a…
The classification and construction of symmetry protected topological (SPT) phases have been intensively studied in interacting systems recently. To our surprise, in interacting fermion systems, there exists a new class of the so-called…
We introduce an index for symmetry protected topological (SPT) phases of infinite fermionic chains with an on-site symmetry given by a finite group $G$. This index takes values in $\mathbb{Z}_2 \times H^1(G,\mathbb{Z}_2) \times H^2(G,…
We present simple lattice realizations of symmetry-protected topological (SPT) phases with $q$-form global symmetries where charged excitations have $q$ spatial dimensions. Specifically, we construct $d$ space-dimensional models supported…
We prove that every unitary invertible quantum field theory satisfies a generalization of the famous spin-statistics theorem. To formulate this extension, we define a `higher spin' action of the stable orthogonal group $O$ on appropriate…
We develop a theoretical framework for the classification and construction of symmetry protected topological (SPT) phases, which are a special class of zero-temperature phases of strongly interacting gapped quantum many-body systems that…
We construct infinitely many new exactly solvable local commuting projector lattice Hamiltonian models for general bosonic beyond group cohomology invertible topological phases of order two and four in any spacetime dimensions, whose…
Reflection positivity originates from one of the Osterwalder-Schrader axioms for constructive quantum field theory. It serves as a bridge between euclidean and relativistic quantum field theory. In mathematics, more specifically, in…
We revisit and extend results by Ueltschi [19] on the application of reflection positivity to loop models with $\theta \in \mathbb{N}_{\geq 2}$. By exploiting additional flexibility in the method, we prove the existence of long loops over a…
We derive a scheme for systematically enumerating the responses of gapped as well as gapless systems of free fermions to electromagnetic and strain fields starting from a common parent theory. Using the fact that position operators in the…
The classification and lattice model construction of symmetry protected topological (SPT) phases in interacting fermion systems are very interesting but challenging. In this paper, we give a systematic fixed point wave function construction…
Clean isotropic quantum Hall fluids in the continuum possess a host of symmetry-protected quantized invariants, such as the Hall conductivity, shift and Hall viscosity. Here we develop a theory of symmetry-protected quantized invariants for…
We present a systematic topological classification of fermionic and bosonic topological phases protected by time-reversal, particle-hole, parity, and combination of these symmetries. We use two complementary approaches: one in terms of…
Recently, it has been shown that two-dimensional bosonic symmetry-protected topological(SPT) phases with on-site unitary symmetry $G$ can be completely classified by the group cohomology class $H^3(G, \mathrm{U}(1))$. Later, group…
We calculate normalization factors and reflection amplitudes in the W-invariant conformal quantum field theories. Using these CFT data we derive vacuum expectation values of exponential fields in affine Toda theories and related perturbed…
Reflection positivity constitutes an integral prerequisite in the Osterwalder-Schrader reconstruction theorem which relates quantum field theories defined on Euclidean space to their Lorentzian signature counterparts. In this work we…
In the realm of invertible symmetry, the topological approach based on classifying spaces dominates the classification of 't Hooft anomalies and symmetry protected topological phases. We explore the alternative algebraic approach based on…
Symmetry protected topological (SPT) phases are gapped short-range-entangled quantum phases with a symmetry G. They can all be smoothly connected to the same trivial product state if we break the symmetry. The Haldane phase of spin-1 chain…
We use the Hamiltonian theory developed by Shankar and Murthy to study a quantum Hall system in a tilted magnetic field. With a finite width of the system in the $z$ direction, the parallel component of the magnetic field introduces…
We present a detailed study of the topological Schwinger model [Phys. Rev. D 99, 014503 (2019)], which describes (1+1) quantum electrodynamics of an Abelian $U(1)$ gauge field coupled to a symmetry-protected topological matter sector, by…