131 citations · 912 across the 45 of their papers we have counts for
51 papers
Free Fermion frustration-free models have zero Hall conductance
Sven Bachmann, Zhiqian Du, Martin Fraas
We give a new proof that translation-invariant free Fermion frustration-free models have zero Hall conductance. Our proof is analytic in nature and it uses the bulk-edge correspond…
Pure gapped ground states of spin chains are short-range entangled
Wojciech De Roeck, Martin Fraas, Bruno de O. Carvalho
We consider spin chains with a finite range Hamiltonian. For reasons of simplicity, the chain is taken to be infinitely long. A ground state is said to be a unique gapped ground st…
Gaussian filters in quantum lattice systems: Applications to spectral flow, local perturbations, clustering, and the quantum Hall effect
Sven Bachmann, Zhiqian, Du +2
We consider the locality and spectral properties of the smearing \[ τ_f(A) = \int_{-\infty}^\infty dt \, f(t) \, τ_t(A) \] when applied to the dynamics of quantum spin system…
Tensor category describing anyons in the quantum Hall effect and quantization of conductance
Sven Bachmann, Matthew Corbelli, Martin Fraas +1
In this study, we examine the quantization of Hall conductance in an infinite plane geometry. We consider a microscopic charge-conserving system with a pure, gapped infinite-volume…
Poincaré disk as a model of squeezed states of a harmonic oscillator
Ian Chi, Martin Fraas, Tina Tan
Single-mode squeezed states exhibit a direct correspondence with points on the Poincaré disk. In this study, we delve into this correspondence and describe the motions of the disk…
Commuting Kraus operators are normal
Martin Fraas
Let be a set of mutually commuting matrices. We show that if then the matrices are normal and, in particular, simu…
A classification of -charge Thouless pumps in 1D invertible states
Sven Bachmann, Wojciech De Roeck, Martin Fraas +1
Recently, a theory has been proposed that classifies cyclic processes of symmetry protected topological (SPT) quantum states. For the case of spin chains, i.e.\ one-dimensional bos…
Derivation of Kubo's formula for disordered systems at zero temperature
Wojciech De Roeck, Alexander Elgart, Martin Fraas
This work justifies the linear response formula for the Hall conductance of a two-dimensional disordered system. The proof rests on controlling the dynamics associated with a rando…
The appearance of particle tracks in detectors -- II: the semi-classical realm
Tristan Benoist, Martin Fraas, Jürg Fröhlich
The appearance of tracks, close to classical orbits, left by charged quantum particles propagating inside a detector, such as a cavity periodically illuminated by light pulses, is…
Stability of invertible, frustration-free ground states against large perturbations
Sven Bachmann, Wojciech De Roeck, Brecht Donvil +1
A gapped ground state of a quantum spin system has a natural length scale set by the gap. This length scale governs the decay of correlations. A common intuition is that this lengt…
On Kitaev's determinant formula
Alexander Elgart, Martin Fraas
We establish a sufficient condition under which for a pair of bounded, invertible operators on a Hilbert space.
The appearance of particle tracks in detectors
Miguel Ballesteros, Tristan Benoist, Martin Fraas +1
The phenomenon that a quantum particle propagating in a detector, such as a Wilson cloud chamber, leaves a track close to a classical trajectory is analyzed. We introduce an ideali…
Exactness of linear response in the quantum Hall effect
Sven Bachmann, Wojciech De Roeck, Martin Fraas +1
In general, linear response theory expresses the relation between a driving and a physical system's response only to first order in perturbation theory. In the context of charge tr…
Rational indices for quantum ground state sectors
Sven Bachmann, Alex Bols, Wojciech De Roeck +1
We consider charge transport for interacting many-body systems with a gapped ground state subspace which is finitely degenerate and topologically ordered. To any locality-preservin…
On the absence of stationary currents
Sven Bachmann, Martin Fraas
We review proofs of a theorem of Bloch on the absence of macroscopic stationary currents in quantum systems. The standard proof shows that the current in 1D vanishes in the large v…
A many-body Fredholm index for ground state spaces and Abelian anyons
Sven Bachmann, Alex Bols, Wojciech De Roeck +1
We propose a many-body index that extends Fredholm index theory to many-body systems. The index is defined for any charge-conserving system with a topologically ordered -dimensi…
Invariant measure for stochastic Schrödinger equations
Tristan Benoist, Martin Fraas, Yan Pautrat +1
Quantum trajectories are Markov processes that describe the time-evolution of a quantum system undergoing continuous indirect measurement. Mathematically, they are defined as solut…
Non-Markovian noise that cannot be dynamically decoupled by periodic spin echo pulses
Daniel Burgarth, Paolo Facchi, Martin Fraas +1
Dynamical decoupling is the leading technique to remove unwanted interactions in a vast range of quantum systems through fast rotations. But what determines the time-scale of such…
Note on linear response for interacting Hall insulators
Sven Bachmann, Alex Bols, Wojciech De Roeck +1
We relate explicitly the adiabatic curvature -- in flux space -- of an interacting Hall insulator with nondegenerate ground state to various linear response coefficients, in partic…
A many-body index for quantum charge transport
Sven Bachmann, Alex Bols, Wojciech De Roeck +1
We propose an index for pairs of a unitary map and a clustering state on many-body quantum systems. We require the map to conserve an integer-valued charge and to leave the state,…
Indirect Measurements of a Harmonic Oscillator
Martin Fraas, Gian Michele Graf, Lisa Hänggli
The measurement of a quantum system becomes itself a quantum-mechanical process once the apparatus is internalized. That shift of perspective may result in different physical predi…
The adiabatic theorem in a quantum many-body setting
Sven Bachmann, Wojciech De Roeck, Martin Fraas
In these lecture notes, we review the adiabatic theorem in quantum mechanics, focusing on a recent extension to many-body systems. The role of locality is emphasized and the relati…
Perturbation Theory for Weak Measurements in Quantum Mechanics, I -- Systems with Finite-Dimensional State Space
M. Ballesteros, N. Crawford, M. Fraas +2
The quantum theory of indirect measurements in physical systems is studied. The example of an indirect measurement of an observable represented by a self-adjoint operator $\mathcal…
Quantization of conductance in gapped interacting systems
Sven Bachmann, Alex Bols, Wojciech De Roeck +1
We provide a short proof of the quantisation of the Hall conductance for gapped interacting quantum lattice systems on the two-dimensional torus. This is not new and should be seen…