13 research outputs found
Hamiltonian simulation of the Schwinger model at finite temperature
Using Matrix Product Operators (MPO) the Schwinger model is simulated in
thermal equilibrium. The variational manifold of gauge invariant MPO is
constructed to represent Gibbs states. As a first application the chiral
condensate in thermal equilibrium is computed and agreement with earlier
studies is found. Furthermore, as a new application the Schwinger model is
probed with a fractional charged static quark-antiquark pair separated
infinitely far from each other. A critical temperature beyond which the string
tension is exponentially suppressed is found, which is in qualitative agreement
with analytical studies in the strong coupling limit. Finally, the CT symmetry
breaking is investigated and our results strongly suggest that the symmetry is
restored at any nonzero temperature.Comment: Updated manuscript matching its published version: more detailed
continuum extrapolation of chiral condensate in section II
Tensor networks for gauge field theories
Over the last decade tensor network states (TNS) have emerged as a powerful
tool for the study of quantum many body systems. The matrix product states
(MPS) are one particular class of TNS and are used for the simulation of
(1+1)-dimensional systems. In this proceeding we use MPS to determine the
elementary excitations of the Schwinger model in the presence of an electric
background field. We obtain an estimate for the value of the background field
where the one-particle excitation with the largest energy becomes unstable and
decays into two other elementary particles with smaller energy.Comment: Proceeding of talk presented at the 33rd International Symposium on
Lattice Field Theory, 14-18 July 2015, Kobe, Japan; Proceeding of talk
presented at The European Physical Society Conference on High Energy Physics,
22-29 July 2015, Vienna, Austria (PoS(EPS-HEP2015)375
Matrix product states for Hamiltonian lattice gauge theories
Over the last decade tensor network states (TNS) have emerged as a powerful
tool for the study of quantum many body systems. The matrix product states
(MPS) are one particular case of TNS and are used for the simulation of 1+1
dimensional systems. In [1] we considered the MPS formalism for the simulation
of the Hamiltonian lattice gauge formulation of 1+1 dimensional one flavor
quantum electrodynamics, also known as the massive Schwinger model. We deduced
the ground state and lowest lying excitations. Furthermore, we performed a full
quantum real-time simulation for a quench with a uniform background electric
field. In this proceeding we continue our work on the Schwinger model. We
demonstrate the advantage of working with gauge invariant MPS by comparing with
MPS simulations on the full Hilbert space, that includes numerous non-physical
gauge variant states. Furthermore, we compute the chiral condensate and recover
the predicted UV-divergent behavior.Comment: presented at the 32nd International Symposium on Lattice Field Theory
(Lattice 2014), 23 - 28 June 2014, New York, US
Finite-representation approximation of lattice gauge theories at the continuum limit with tensor networks
It has been established that matrix product states can be used to compute the ground state and single-particle excitations and their properties of lattice gauge theories at the continuum limit. However, by construction, in this formalism the Hilbert space of the gauge fields is truncated to a finite number of irreducible representations of the gauge group. We investigate quantitatively the influence of the truncation of the infinite number of representations in the Schwinger model, one-flavor QED 2, with a uniform electric background field. We compute the two-site reduced density matrix of the ground state and the weight of each of the representations. We find that this weight decays exponentially with the quadratic Casimir invariant of the representation which justifies the approach of truncating the Hilbert space of the gauge fields. Finally, we compute the single-particle spectrum of the model as a function of the electric background field
Matrix product states for gauge field theories
The matrix product state formalism is used to simulate Hamiltonian lattice
gauge theories. To this end, we define matrix product state manifolds which are
manifestly gauge invariant. As an application, we study 1+1 dimensional one
flavour quantum electrodynamics, also known as the massive Schwinger model, and
are able to determine very accurately the ground state properties and
elementary one-particle excitations in the continuum limit. In particular, a
novel particle excitation in the form of a heavy vector boson is uncovered,
compatible with the strong coupling expansion in the continuum. We also study
non-equilibrium dynamics by simulating the real-time evolution of the system
induced by a quench in the form of a uniform background electric field.Comment: expanded discussion on real-time evolution, matching the published
versio
Real-time simulation of the Schwinger effect with Matrix Product States
Matrix Product States (MPS) are used for the simulation of the real-time
dynamics induced by an electric quench on the vacuum state of the massive
Schwinger model. For small quenches it is found that the obtained oscillatory
behavior of local observables can be explained from the single-particle
excitations of the quenched Hamiltonian. For large quenches damped oscillations
are found and comparison of the late time behavior with the appropriate Gibbs
states seems to give some evidence for the onset of thermalization. Finally,
the MPS real-time simulations are explicitly compared with the semi-classical
approach and, as expected, agreement is found in the limit of large quenches.Comment: Small changes, matching its published versio
Confinement and String Breaking for QED_{2} in the Hamiltonian Picture
The formalism of matrix product states is used to perform a numerical study of (1+1)-dimensional QED—also known as the (massive) Schwinger model—in the presence of an external static “quark” and “antiquark”. We obtain a detailed picture of the transition from the confining state at short interquark distances to the broken-string “hadronized” state at large distances, and this for a wide range of couplings, recovering the predicted behavior both in the weak- and strong-coupling limit of the continuum theory. In addition to the relevant local observables like charge and electric field, we compute the (bipartite) entanglement entropy and show that subtraction of its vacuum value results in a UV-finite quantity. We find that both string formation and string breaking leave a clear imprint on the resulting entropy profile. Finally, we also study the case of fractional probe charges, simulating for the first time the phenomenon of partial string breaking