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Chiral condensate in the Schwinger model with Matrix Product Operators · Around

2016

Chiral condensate in the Schwinger model with Matrix Product Operators

Bañuls, Mari Carmen, Cichy, Krzysztof, Jansen, Karl et al.

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Tensor network (TN) methods, in particular the Matrix Product States (MPS) ansatz, have proven to be a useful tool in analyzing the properties of lattice gauge theories.

They allow for a very good precision, much better than standard Monte Carlo (MC) techniques for the models that have been studied so far, due to the possibility of reaching much smaller lattice spacings.
The real reason for the interest in the TN approach, however, is its ability, shown so far in several condensed matter models, to deal with theories which exhibit the notorious sign problem in MC simulations.
This makes it prospective for dealing with the non-zero chemical potential in QCD and other lattice gauge theories, as well as with real-time simulations.

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G. D. las Cuevas, N. Schuch, D. Pérez-García, and J. I. Cirac, Purifications of multipartite states: limitations and constructive methods
Original
1914
Earlier work this paper cites.
H. F. Trotter, On the product of semi-groups of operators
1959
Earlier work this paper cites.
J. Schwinger, Gauge Invariance and Mass. II
1962
Earlier work this paper cites.
Dover, New York, 1964
M. Abramowitz and I. Stegun, Handbook of Mathematical Functions · 1964
Earlier work this paper cites.
M.-D. Choi, Completely positive linear maps on complex matrices
1975
Earlier work this paper cites.
T. Banks, L. Susskind, and J. B. Kogut, Strong Coupling Calculations of Lattice Gauge Theories: (1+1)-Dimensional Exercises
1976
Earlier work this paper cites.
M. Suzuki, Fractal decomposition of exponential operators with applications to many-body theories and monte carlo simulations
1990
Earlier work this paper cites.
S. R. White, Density matrix formulation for quantum renormalization groups
1992
Earlier work this paper cites.
I. Sachs and A. Wipf, Finite temperature Schwinger model
Original
1992
Earlier work this paper cites.
Y. Hosotani and R. Rodriguez, Bosonized massive N flavor Schwinger model
1998
Earlier work this paper cites.
P. de Forcrand, J. Hetrick, T. Takaishi, and A. van der Sijs, Three topics in the Schwinger model
1998
Earlier work this paper cites.
T. Byrnes, P. Sriganesh, R. Bursill, and C. Hamer, Density matrix renormalization group approach to the massive Schwinger model
2002
Earlier work this paper cites.
F. Verstraete, D. Porras, and J. I. Cirac, Density matrix renormalization group and periodic boundary conditions: A quantum information perspective
2004
Earlier work this paper cites.
G. Vidal, Efficient simulation of one-dimensional quantum many-body systems
2004
Earlier work this paper cites.
F. Verstraete, J. J. García-Ripoll, and J. I. Cirac, Matrix product density operators: Simulation of finite-temperature and dissipative systems
2004
Earlier work this paper cites.

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