Tensor network methods for lattice gauge theories
Final Report Abstract
The project concerned the use of quantum-information-inspired tensor network (TN) methods to investigate properties of lattice gauge theories. Our preliminary work on this topic, before realizing this grant, showed that the methods can provide a successful and precise description of the underlying physics and our aim in the project was to make the natural next steps in pursuit of applying them for the case of the theory of the strong interaction, quantum chromodynamics (QCD). QCD is non-perturbative in the low-energy regime and quantitative predictions from first principles can only be obtained using the lattice regularization and Monte Carlo (MC) techniques to evaluate the relevant path integrals. However, MC simulations are plagued by the sign problem in certain physical situations, such as including a non-zero chemical potential or real-time simulations. Hence, alternatives for MC are sought for and one such alternative can be TN methods, by construction devoid of the sign problem. In the project, we further investigated the Schwinger model, concentrating on finite temperature properties and non-zero chemical potential. The latter was the first demonstration that TN methods can indeed overcome the sign problem and provide reliable and precise results. We reproduced several analytical results in the massless case and we obtained new ones at non-zero fermion masses. In particular, we investigated the first order phase transitions between phases with different particle numbers and we provided the phase diagram in the isospin chemical potential vs. fermion mass plane in the two-flavour Schwinger model. Moreover, since QCD is non-Abelian, we extended our study to the non-Abelian SU(2) gauge theory, another toy model of QCD. We devised an efficient basis for this case, extensible also to other gauge groups and relevant from the point of view of quantum simulations, currently planned in Innsbruck. We investigated the spectrum of the SU(2) theory and determined the scaling exponent in the mass dependence of the vector boson mass, finding a result compatible with the large-Nc expansion of Steinhardt. We also analyzed entanglement properties of this theory and revealed its relation with a conformal field theory with central charge c = 2, according to the celebrated Calabrese-Cardy hypothesis. As of now, the work on project topics is continued, with several theories in mind, most notably the 1+1-dimensional QCD and 2+1-dimensional quantum electrodynamics (QED). Realizing this aim will be another crucial step in the quest of applying TN methods for QCD in 3+1 dimensions. Although this is a very difficult task, the progress achieved in this DFG grant, combined with recent theoretical developments, make such an application realistic and pave the way for next steps in the quest.
Publications
- Chiral condensate in the Schwinger model with Matrix Product Operators, Phys. Rev. D 93 (2016) no.9, 094512
M. C. Bañuls, K. Cichy, K. Jansen and H. Saito
- Density Induced Phase Transitions in the Schwinger Model: A Study with Matrix Product States, Phys. Rev. Lett. 118 (2017) 071601
M. C. Bañuls, K. Cichy, J. I. Cirac, K. Jansen and S. Kühn
- Efficient basis formulation for 1+1 dimensional SU(2) lattice gauge theory: Spectral calculations with matrix product states, Phys. Rev. X 7 (2017) 041046
M. C. Bañuls, K. Cichy, J. I. Cirac, K. Jansen and S. Kühn
- Towards overcoming the Monte Carlo sign problem with tensor networks, EPJ Web Conf. 137 (2017) 04001
M. C. Bañuls, K. Cichy, J. I. Cirac, K. Jansen, S. Kühn and H. Saito
