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In these lecture notes, we review some recent works on Hamiltonian lattice gauge theories, that involve, in particular, tensor network methods.
P. Silvi, Y. Sauer, F. Tschirsich and S. Montangero, · 1901
Earlier work this paper cites.
Ultraviolet Behavior of Non-Abelian Gauge Theories ,
D. J. Gross and F. Wilczek, · 1973
Earlier work this paper cites.
Confinement of quarks ,
K. G. Wilson, · 1974
Earlier work this paper cites.
Hamiltonian formulation of Wilson’s lattice gauge theories ,
J. Kogut and L. Susskind, · 1975
Earlier work this paper cites.
Lattice fermions ,
L. Susskind, · 1977
Earlier work this paper cites.
An introduction to lattice gauge theory and spin systems ,
J. B. Kogut, · 1979
Earlier work this paper cites.
Phase diagrams of lattice gauge theories with Higgs fields ,
E. Fradkin and S. H. Shenker, · 1979
Earlier work this paper cites.
Duality in field theory and statistical systems ,
R. Savit, · 1980
Earlier work this paper cites.
Decomposition formulas of exponential operators and Lie exponentials with some applications to quantum mechanics and statistical physics ,
M. Suzuki, · 1985
Earlier work this paper cites.
Density matrix formulation for quantum renormalization groups ,
S. R. White, · 1992
Earlier work this paper cites.
An Introduction to Quantum Field Theory ,
M. E. Peskin and D. V. Schroeder, · 1995
Earlier work this paper cites.
Universal Quantum Simulators ,
S. Lloyd, · 1996
Earlier work this paper cites.
Density matrix renormalization group approach to the massive Schwinger model ,
T. M. R. Byrnes, P. Sriganesh, R. J. Bursill and C. J. Hamer, · 2002
Earlier work this paper cites.
Computational Complexity and Fundamental Limitations to Fermionic Quantum Monte Carlo Simulations ,
M. Troyer and U.-J. Wiese, · 2005
Earlier work this paper cites.
Lagrangian representation for fermionic linear optics ,
S. Bravyi, · 2005
Earlier work this paper cites.
Matrix product representation of gauge invariant states in a ℤ 2 \mathbb{Z}_{2} lattice gauge theory ,
T. Sugihara, · 2005
Earlier work this paper cites.
Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems ,
F. Verstraete, V. Murg and J. Cirac, · 2008
Earlier work this paper cites.
Entanglement entropy in gauge theories and the holographic principle for electric strings ,
P. Buividovich and M. Polikarpov, · 2008
Earlier work this paper cites.
Fermionic projected entangled pair states ,
C. V. Kraus, N. Schuch, F. Verstraete and J. I. Cirac, · 2010
Earlier work this paper cites.
The phase diagram of dense QCD ,
K. Fukushima and T. Hatsuda, · 2011
Earlier work this paper cites.
Entanglement renormalization and gauge symmetry ,
L. Tagliacozzo and G. Vidal, · 2011
Earlier work this paper cites.
Ultracold quantum gases and lattice systems: Quantum simulation of lattice gauge theories ,
U.-J. Wiese, · 2013
Cited alongside, same era.
The mass spectrum of the Schwinger model with matrix product states ,
M. Bañuls, K. Cichy, J. Cirac and K. Jansen, · 2013
Cited alongside, same era.
Review of lattice results concerning low-energy particle physics ,
FLAG Working Group, S. Aoki, Y. Aoki, C. Bernard, T. Blum, G. Colangelo, M. Della Morte, S. Dürr, A. X. El-Khadra, H. Fukaya, R. Horsley, A. Jüttner et al. , · 2014
Cited alongside, same era.
A practical introduction to tensor networks: Matrix product states and projected entangled pair states ,
R. Orús, · 2014
Cited alongside, same era.
Tensor Networks for Lattice Gauge Theories with Continuous Groups ,
L. Tagliacozzo, A. Celi and M. Lewenstein, · 2014
Cited alongside, same era.
Matrix Product States for Gauge Field Theories ,
Real-Time Dynamics in U(1) Lattice Gauge Theories with Tensor Networks ,
T. Pichler, M. Dalmonte, E. Rico, P. Zoller and S. Montangero, · 2016
Later among the works it cites.
Matrix product states and the non-Abelian rotor model ,
A. Milsted, · 2016
Later among the works it cites.
Hamiltonian simulation of the Schwinger model at finite temperature ,
B. Buyens, F. Verstraete and K. Van Acoleyen, · 2016
Later among the works it cites.
M. Bañuls, K. Cichy, J. Cirac, K. Jansen, S. Kühn and H. Saito, · 2016
Later among the works it cites.
Digital Quantum Simulation of Z 2 Lattice Gauge Theories with Dynamical Fermionic Matter ,
E. Zohar, A. Farace, B. Reznik and J. I. Cirac, · 2017
Later among the works it cites.
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B. Buyens, J. Haegeman, K. Van Acoleyen, H. Verschelde and F. Verstraete, · 2014
Cited alongside, same era.
Lattice gauge tensor networks ,
P. Silvi, E. Rico, T. Calarco and S. Montangero, · 2014
Cited alongside, same era.
Tensor Networks for Lattice Gauge Theories and Atomic Quantum Simulation ,
E. Rico, T. Pichler, M. Dalmonte, P. Zoller and S. Montangero, · 2014
Cited alongside, same era.
H. Saito, M. C. Bañuls, K. Cichy, J. I. Cirac and K. Jansen, · 2014
Cited alongside, same era.
Fermionic projected entangled pair states and local U(1) gauge theories ,
E. Zohar, M. Burrello, T. B. Wahl and J. I. Cirac, · 2015
Cited alongside, same era.
Formulation of lattice gauge theories for quantum simulations ,
E. Zohar and M. Burrello, · 2015
Cited alongside, same era.
Gauging Quantum States: From Global to Local Symmetries in Many-Body Systems ,
J. Haegeman, K. Van Acoleyen, N. Schuch, J. I. Cirac and F. Verstraete, · 2015
Cited alongside, same era.
E. Zohar, A. Farace, B. Reznik and J. I. Cirac, · 2017
Later among the works it cites.
Hand-waving and Interpretive Dance: An Introductory Course on Tensor Networks ,
J. C. Bridgeman and C. T. Chubb, · 2017
Later among the works it cites.
Finite-density phase diagram of a ( 1 + 1 ) - d non-abelian lattice gauge theory with tensor networks ,
P. Silvi, E. Rico, M. Dalmonte, F. Tschirsich and S. Montangero, · 2017
Later among the works it cites.
Real-time simulation of the Schwinger effect with matrix product states ,
B. Buyens, J. Haegeman, F. Hebenstreit, F. Verstraete and K. Van Acoleyen, · 2017
Later among the works it cites.
Density Induced Phase Transitions in the Schwinger Model: A Study with Matrix Product States ,
M. C. Bañuls, K. Cichy, J. I. Cirac, K. Jansen and S. Kühn, · 2017
Later among the works it cites.
Towards overcoming the Monte Carlo sign problem with tensor networks ,
Bañuls, Mari Carmen, Cichy, Krzysztof, Ignacio Cirac, J., Jansen, Karl, Kühn, Stefan and Saito, Hana, · 2017
Later among the works it cites.
Efficient Basis Formulation for ( 1 + 1 )-Dimensional SU(2) Lattice Gauge Theory: Spectral Calculations with Matrix Product States ,
M. C. Bañuls, K. Cichy, J. I. Cirac, K. Jansen and S. Kühn, · 2017
Later among the works it cites.
Combining tensor networks with Monte Carlo methods for lattice gauge theories ,
E. Zohar and J. I. Cirac, · 2018
Closest in time.
Eliminating fermionic matter fields in lattice gauge theories ,
E. Zohar and J. I. Cirac, · 2018
Closest in time.
Digital quantum simulation of lattice gauge theories in three spatial dimensions ,
J. Bender, E. Zohar, A. Farace and J. I. Cirac, · 2018
Closest in time.
Tensor Network study of the (1+1)-dimensional Thirring Model ,
M. Carmen Bañuls, K. Cichy, Y.-J. Kao, C.-J. David Lin, Y.-P. Lin and D. Tao-Lin Tan, · 2018
Closest in time.
Tensor Networks and their use for Lattice Gauge Theories ,
M. C. Bañuls, K. Cichy, J. I. Cirac, K. Jansen and S. Kühn, · 2018
Closest in time.
Removing staggered fermionic matter in U ( N ) U(N) and S U ( N ) SU(N) lattice gauge theories ,
E. Zohar and J. I. Cirac, · 2019
Closest in time.
The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems ,
P. Silvi, F. Tschirsich, M. Gerster, J. Jünemann, D. Jaschke, M. Rizzi and S. Montangero, · 2019
Closest in time.
Phase diagram and conformal string excitations of square ice using gauge invariant matrix product states ,
F. Tschirsich, S. Montangero and M. Dalmonte, · 2019
Closest in time.