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Register a new userNumerical investigations of the Schwinger model and selected quantum spin models
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Added by
Marcin Szyniszewski
Publication date
2013
fields
Physics
and research's language is
English
Authors
Marcin Szyniszewski
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Numerical investigations of the XY model, the Heisenberg model and the J-J Heisenberg model are conducted, using the exact diagonalisation, the numerical renormalisation and the density matrix renormalisation group approach. The low-lying energy levels are obtained and finite size scaling is performed to estimate the bulk limit values. The results are found to be consistent with the exact values. The DMRG results are found to be most promising. The Schwinger model is also studied using the exact diagonalisation and the strong coupling expansion. The massless, the massive model and the model with a background electric field are explored. Ground state energy, scalar and vector particle masses and order parameters are examined. The achieved values are observed to be consistent with previous results and theoretical predictions. Path to the future studies is outlined.
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Using a recently introduced tensor network method, we study the density of states of the lattice Schwinger model, a standard testbench for lattice gauge theory numerical techniques, but also the object of recent experimental quantum simulations. We identify regimes of parameters where the spectrum appears to be symmetric and displays the expected continuum properties even for finite lattice spacing and number of sites. However, we find that for moderate system sizes and lattice spacing of $gasim O(1)$, the spectral density can exhibit very different properties with a highly asymmetric form. We also explore how the method can be exploited to extract thermodynamic quantities.
We construct a tensor network representation of the partition function for the massless Schwinger model on a two dimensional lattice using staggered fermions. The tensor network representation allows us to include a topological term. Using a particular implementation of the tensor renormalization group (HOTRG) we calculate the phase diagram of the theory. For a range of values of the coupling to the topological term $theta$ and the gauge coupling $beta$ we compare with results from hybrid Monte Carlo when possible and find good agreement.
We perform a digital quantum simulation of a gauge theory with a topological term in Minkowski spacetime, which is practically inaccessible by standard lattice Monte Carlo simulations. We focus on $1+1$ dimensional quantum electrodynamics with the $theta$-term known as the Schwinger model. We construct the true vacuum state of a lattice Schwinger model using adiabatic state preparation which, in turn, allows us to compute an expectation value of the fermion mass operator with respect to the vacuum. Upon taking a continuum limit we find that our result in massless case agrees with the known exact result. In massive case, we find an agreement with mass perturbation theory in small mass regime and deviations in large mass regime. We estimate computational costs required to take a reasonable continuum limit. Our results imply that digital quantum simulation is already useful tool to explore non-perturbative aspects of gauge theories with real time and topological terms.
We investigate the continuum limit scaling of the scalar condensate in the $N_f=2$ Schwinger model on the lattice. We employ maximally twisted mass Wilson fermions and overlap fermions. We compute the scalar condensate by taking the trace of the propagator (direct method) and by utilizing the integrated Ward-Takahashi identity. While the scalar condensate comes out consistent using these two methods for a given kind of lattice fermions, we find --quite surprisingly-- large discrepancies for the scalar condensate between twisted mass and overlap fermions. These discrepancies are only resolved when using the point split current for twisted mass fermions.
Quantum spin and quantum link models provide an unconventional regularization of field theory in which classical fields arise via dimensional reduction of discrete variables. This D-theory regularization leads to the same continuum theories as the conventional approach. We show this by deriving the low-energy effective Lagrangians of D-theory models using coherent state path integral techniques. We illustrate our method for the $(2+1)$-d Heisenberg quantum spin model which is the D-theory regularization of the 2-d O(3) model. Similarly, we prove that in the continuum limit a $(2+1)$-d quantum spin model with $SU(N)_Ltimes SU(N)_Rtimes U(1)_{L=R}$ symmetry is equivalent to the 2-d principal chiral model. Finally, we show that $(4+1)$-d SU(N) quantum link models reduce to ordinary 4-d Yang-Mills theory.
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