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Report

Teaser, summary, work performed and final results

Periodic Reporting for period 1 - QSIMCORR (Quantum Simulation of Strongly-Correlated Systems)

Teaser

Summary

A major challenge in theoretical physics is to develop novel methods without systematic errors. The scope of this proposal is the numerical control over strongly correlated phases in the thermodynamic limit through two main developments:

First, for bosonic systems, we aim to obtain reliable phase diagrams for optical flux lattices, combining topology with interactions. In particular, we study the competition between superfluid order and (fractional) Chern insulators, which may harbor (non-)abelian anyonic excitations. This is achieved by a major improvement on our current selfenergy-based cluster methods through non-local interactions, vertex corrections and momentum cluster extensions.

Second, for fermionic systems with long-range interactions, such as warm dense matter, the electron gas, and cold gases with Rydberg interactions, the diagrammatic Monte Carlo method is uniquely situated to compute thermal exchange correlation energies over the entire density range, essential to any calculation in condensed matter physics, astro physics and plasma physics. It employs a universal language but needs further algorithmic refinements for improving its convergence and sign properties. Extensions are towards (frustrated) spin systems, providing an alternative route to the realization of strongly correlated phases.

At all stages analytical derivations must be supplemented with coding and high-performance computation. Simultaneously, we seek to extend the paradigm of quantum simulation by comparing the results of our novel methods with cold gas experiments in challenging regimes, where possible.

Work performed

\"Main Results:

Main results:
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(i) The interplay between magnetism and doping is at the heart of strongly correlated physics in the cuprates and notoriously hard to study theoretically. In Nature 565, 56-60 (2019) incommensurate magnetism in Hubbard chains (one dimension) could unambiguously be measured experimentally thanks to single-site spin-resolved detection tools (a so-called quantum microscope). The results are in good agreement with our theoretical modelling. The correlations were seen to extend over just a couple of sites because of finite temperature effects. These results pave the way to study the interplay between doping and magnetism in two dimensions, and to study signatures of magnetic polarons.

(ii) It is known since the noble-price winning work by Kosterlitz, Thouless and others that superfluidity in two dimensions can be destroyed by a mechanism known as vortex pair unbinding, which is topological in nature. No other mechanism is known. However, in analogy to the strong disorder scenario in one dimension at zero temperature, \"\"scratches\"\" could be shown to provide an alternative route to the destruction of superfluidity, which can preempt the vortex pair unbinding scenario. This was shown numerically in Phys Rev B 99, 104514 (2019) and confirmed our controlled renormalization group analysis. A particular facet is the choice of the microscopic model which minimizes the finite size effects to a minimum (and which we were unable to find for the quantum problem in the past). The figure \"\"scratchedXY.png\"\" (copyright APS, Phys Rev B 99, 104514 (2019)) shows a Weber-Minnhagen fit clearly indicating that the transition belongs to the novel scratched-XY class, and not to the traditional Kosterlitz-Thouless type.

(iii) Artificial Intelligence is rapidly influencing our daily life: facial recognition at airports, autonomous driving, better detection of cancerous tissue, and unbeatable chess or go computers are just a few examples that one has most likely already encountered. But can machines also be useful for the condensed matter physicist? This we can answer in the affirmative: We developed in a series of papers a tensorial-kernel support vector machine capable of determining the phase diagram of the classical XXZ model on the pyrochlore lattice (Phys Rev B 99, 060404 (2019), Phys Rev B 99, 104410 (2019), and arXiv:1907.12322 (PRB, in press), and one Editorâ€™s Suggestion). This machine is interpretable in the sense that the order parameter (which can be a tensor of high rank) can be deduced straightforwardly from the output of the machine. The machine is also capable of finding emergent constraints which may hint at an underlying gauge structure and identify candidates for spin liquid phases. Our implementation of the method belongs only semantically to the realm of supervised learning: it is possible to perform a graph spectral analysis and identify the relevant regimes in parameter space based on the bias parameter of the decision function, which could be shown to have physical meaning and thereby avoid a learning phase of the phases that have to be identified. The resulting phase diagram is shown in \"\"SVM_pyrochlore.png\"\" (arXiv:1907.12322) :from the graph spectral spectral analysis (in blue, upper part) one recognizes 6 different parameter regimes. The machine subsequently analyzes the pooled data further and finds two symmetry broken phases (an antiferromagnet in the lower right corner and a biaxial spin nematic in the lower left corner) and several spin liquid phases in between, including spin ice.

Other work performed:
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(i) We developed stochastic lists for the simulation of multi-variable functions with population methods (Phys Rev B 98, 085102 (2018)) where we showed that a multi-dimensional object such as a vertex in quantum field theory can be represented by a stochastic list of coordinates that have to be sampled over instead of stored on a multi-dimensional gri\"

Final results

\"Beyond state of the art: see \"\"main results\"\" aboive

Expected results:
- applying the tensorial-kernel support vector machine to an unsolved classical problem
- extension of the tensortial-kernel support vector machine to certain classes quantum problems
- deeper insight in Fermi polaron mobilities: can one obtain results without resorting to analytic continuation?
- developments (determinants and convergence issues) of diagramatic Monte Carlo simulations for quantum field theories
- new insight in bosonic symmetry protected phases through the development of new solvers and methods\"