Finite-density phase diagram of a $(1+1)-d$ non-abelian lattice gauge theory with tensor networks

Pietro Silvi1,2, Enrique Rico3, Marcello Dalmonte4,5, Ferdinand Tschirsich1, and Simone Montangero1,6

1Institute for complex quantum systems & Center for Integrated Quantum Science and Technologies (IQST), Universität Ulm, D-89069 Ulm, Germany
2Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria
3Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, E-48080 Bilbao, Spain & IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, E-48013 Bilbao, Spain
4Institute for Theoretical Physics, University of Innsbruck, A-6020, Innsbruck, Austria & Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, A-6020 Innsbruck, Austria
5Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, Trieste, Italy
6Institute for Complex Quantum Systems & Center for Integrated Quantum Science and Technologies, Universität Ulm, D- 89069 Ulm, Germany

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Abstract

We investigate the finite-density phase diagram of a non-abelian $SU(2)$ lattice gauge theory in $(1+1)$-dimensions using tensor network methods. We numerically characterise the phase diagram as a function of the matter filling and of the matter-field coupling, identifying different phases, some of them appearing only at finite densities. For weak matter-field coupling we find a meson BCS liquid phase, which is confirmed by second-order analytical perturbation theory. At unit filling and for strong coupling, the system undergoes a phase transition to a charge density wave of single-site (spin-0) mesons via spontaneous chiral symmetry breaking. At finite densities, the chiral symmetry is restored almost everywhere, and the meson BCS liquid becomes a simple liquid at strong couplings, with the exception of filling two-thirds, where a charge density wave of mesons spreading over neighbouring sites appears. Finally, we identify two tri-critical points between the chiral and the two liquid phases which are compatible with a $SU(2)_2$ Wess-Zumino-Novikov-Witten model. Here we do not perform the continuum limit but we explicitly address the global $U(1)$ charge conservation symmetry.

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[1] Mari Carmen Bañuls, Krzysztof Cichy, J. Ignacio Cirac, Karl Jansen, and Stefan Kühn, "Efficient Basis Formulation for ( 1+1 )-Dimensional SU(2) Lattice Gauge Theory: Spectral Calculations with Matrix Product States", Physical Review X 7 4, 041046 (2017).

[2] Alessio Celi, "Different models of gravitating Dirac fermions in optical lattices", The European Physical Journal Special Topics 226 12, 2729 (2017).

[3] Erez Zohar and J. Ignacio Cirac, "Combining tensor networks with Monte Carlo methods for lattice gauge theories", Physical Review D 97 3, 034510 (2018).

[4] Mari Carmen Bañuls, Krzysztof Cichy, Ying-Jer Kao, C.-J. David Lin, Yu-Ping Lin, and David T.-L. Tan, "Phase structure of the ( 1+1 )-dimensional massive Thirring model from matrix product states", Physical Review D 100 9, 094504 (2019).

[5] Román Orús, "Tensor networks for complex quantum systems", Nature Reviews Physics 1 9, 538 (2019).

[6] Daniel C. Hackett, Kiel Howe, Ciaran Hughes, William Jay, Ethan T. Neil, and James N. Simone, "Digitizing gauge fields: Lattice Monte Carlo results for future quantum computers", Physical Review A 99 6, 062341 (2019).

[7] Boye Buyens, Jutho Haegeman, Florian Hebenstreit, Frank Verstraete, and Karel Van Acoleyen, "Real-time simulation of the Schwinger effect with matrix product states", Physical Review D 96 11, 114501 (2017).

[8] Christian Schweizer, Fabian Grusdt, Moritz Berngruber, Luca Barbiero, Eugene Demler, Nathan Goldman, Immanuel Bloch, and Monika Aidelsburger, "Floquet approach to ℤ2 lattice gauge theories with ultracold atoms in optical lattices", Nature Physics 15 11, 1168 (2019).

[9] Pietro Silvi, Yannick Sauer, Ferdinand Tschirsich, and Simone Montangero, "Tensor network simulation of an SU(3) lattice gauge theory in 1D", Physical Review D 100 7, 074512 (2019).

[10] Mari Carmen Bañuls, Rainer Blatt, Jacopo Catani, Alessio Celi, Juan Ignacio Cirac, Marcello Dalmonte, Leonardo Fallani, Karl Jansen, Maciej Lewenstein, Simone Montangero, Christine A. Muschik, Benni Reznik, Enrique Rico, Luca Tagliacozzo, Karel Van Acoleyen, Frank Verstraete, Uwe-Jens Wiese, Matthew Wingate, Jakub Zakrzewski, and Peter Zoller, "Simulating lattice gauge theories within quantum technologies", The European Physical Journal D 74 8, 165 (2020).

[11] Kai Zapp and Román Orús, "Tensor network simulation of QED on infinite lattices: Learning from (1+1) d , and prospects for (2+1) d", Physical Review D 95 11, 114508 (2017).

[12] Ashley Milsted and Tobias J. Osborne, "Quantum Yang-Mills theory: An overview of a program", Physical Review D 98 1, 014505 (2018).

[13] Mari Carmen Bañuls and Krzysztof Cichy, "Review on novel methods for lattice gauge theories", Reports on Progress in Physics 83 2, 024401 (2020).

[14] Patrick Emonts and Erez Zohar, "Gauss law, minimal coupling and fermionic PEPS for lattice gauge theories", SciPost Physics Lecture Notes 12 (2020).

[15] Ilya Kull, Andras Molnar, Erez Zohar, and J. Ignacio Cirac, "Classification of matrix product states with a local (gauge) symmetry", Annals of Physics 386, 199 (2017).

[16] Ferdinand Tschirsich, Simone Montangero, and Marcello Dalmonte, "Phase diagram and conformal string excitations of square ice using gauge invariant matrix product states", SciPost Physics 6 3, 028 (2019).

[17] Falk Bruckmann, Karl Jansen, and Stefan Kühn, "O(3) nonlinear sigma model in 1+1 dimensions with matrix product states", Physical Review D 99 7, 074501 (2019).

[18] Boye Buyens, Simone Montangero, Jutho Haegeman, Frank Verstraete, and Karel Van Acoleyen, "Finite-representation approximation of lattice gauge theories at the continuum limit with tensor networks", Physical Review D 95 9, 094509 (2017).

[19] Erez Zohar, Thorsten B. Wahl, Michele Burrello, and J. Ignacio Cirac, "Projected Entangled Pair States with non-Abelian gauge symmetries: An SU(2) study", Annals of Physics 374, 84 (2016).

[20] Mari Carmen Bañuls, Krzysztof Cichy, J. Ignacio Cirac, Karl Jansen, and Stefan Kühn, "Density Induced Phase Transitions in the Schwinger Model: A Study with Matrix Product States", Physical Review Letters 118 7, 071601 (2017).

[21] Ian C. Cloët, Matthew R. Dietrich, John Arrington, Alexei Bazavov, Michael Bishof, Adam Freese, Alexey V. Gorshkov, Anna Grassellino, Kawtar Hafidi, Zubin Jacob, Michael McGuigan, Yannick Meurice, Zein-Eddine Meziani, Peter Mueller, Christine Muschik, James Osborn, Matthew Otten, Peter Petreczky, Tomas Polakovic, Alan Poon, Raphael Pooser, Alessandro Roggero, Mark Saffman, Brent VanDevender, Jiehang Zhang, and Erez Zohar, "Opportunities for Nuclear Physics & Quantum Information Science", arXiv:1903.05453.

[22] M. C. Banuls, K. Cichy, J. I. Cirac, K. Jansen, S. Kühn, and H. Saito, "The multi-flavor Schwinger model with chemical potential - Overcoming the sign problem with Matrix Product States", Proceedings of the 34th annual International Symposium on Lattice Field Theory (LATTICE2016). 24-30 July 2016. University of Southampton 316 (2016).

[23] Mari Carmen Bañuls, Krzysztof Cichy, J. Ignacio Cirac, Karl Jansen, Stefan Kühn, and Hana Saito, "Towards overcoming the Monte Carlo sign problem with tensor networks", European Physical Journal Web of Conferences 137, 04001 (2017).

[24] Mari Carmen Bañuls, Krzysztof Cichy, Ying-Jer Kao, C. -J. David Lin, Yu-Ping Lin, and David Tao-Lin Tan, "Tensor Network study of the (1+1)-dimensional Thirring Model", arXiv:1710.09993.

[25] Mari Carmen Bañuls, Krzysztof Cichy, Ying-Jer Kao, C. -J. David Lin, Yu-Ping Lin, and David Tao-Lin Tan, "Tensor Network study of the (1+1)-dimensional Thirring Model", European Physical Journal Web of Conferences 175, 11017 (2018).

[26] Adrian Franco-Rubio and Guifre Vidal, "Entanglement renormalization for gauge invariant quantum fields", arXiv:1910.11815.

[27] Zohreh Davoudi, Indrakshi Raychowdhury, and Andrew Shaw, "Search for Efficient Formulations for Hamiltonian Simulation of non-Abelian Lattice Gauge Theories", arXiv:2009.11802.

[28] Yannick Meurice, Ryo Sakai, and Judah Unmuth-Yockey, "Tensor field theory with applications to quantum computing", arXiv:2010.06539.

The above citations are from Crossref's cited-by service (last updated successfully 2020-10-19 20:04:19) and SAO/NASA ADS (last updated successfully 2020-10-19 20:04:21). The list may be incomplete as not all publishers provide suitable and complete citation data.