Lode Pollet

Theoretical Nanophysics

Ludwig-Maximilians-Universität München

Theresienstr. 37

80333 Munich

Tel. +49 89 2180 4593


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Research focus: computational methods, ultracold atoms, quantum many-body physics

The research in our group is situated at the boundary between cold gases, condensed matter and computational physics. We are interested in first principles quantitative approaches to strongly correlated many-body systems. Combining these three fields often offers a new perspective on long-standing problems.

Cold Gases

Cold gases are systems that are ideally suited to implement prototypical strongly-correlated models in an experiment thanks to their cleanliness, tunability and the control one has over them. In other words, they can be used as quantum simulators. We are interested in a quantitative description of such systems in order to perform the necessary benchmarking steps of these analog devices. This has been successfully undertaken for a variety of systems in different contexts.

In the picture, a comparison between simulations and experiment is shown for time-of-flight images of the three-dimensional Bose-Hubbard model for 5 different temperatures. The lack of any visible difference between the two results shows the degree of control we have over these systems. See more in the original publication .

Condensed Matter

Regarding condensed matter physics we study the properties of Helium-4 and supersolids. A supersolid is an elusive phase of matter that simultaneously displays crystalline and superfluid order. According to quantum mechanics, this is perfectly allowed, but hard to find experimentally. Solid Helium-4 had been suggested as a prime candidate, but consensus is growing that it remains an insulator. However, such defects as grain boundaries and dislocations may under certain conditions support superflow. Disordered bosonic systems are also of special interest to us, featuring the Bose glass phase, which is compressible and gapless but nevertheless an insulator. We are also working on dimensional crossovers, both for bosons and fermions, which are relevant for low-dimensional (super)conductors and have recently started investigating Renyi entropies and entanglement properties.

Numerical Methods

Often algorithmic and technical advances in numerical methods are needed in order to arrive at new results. These methods include path integral Monte Carlo (PIMC) with worm-type updates, determinant Monte Carlo (detMC), diagrammatic Monte Carlo (diagMC), and dynamical mean-field theory (DMFT) and cluster extensions for bosons and fermions. PIMC works extremely well for bosonic systems, whereas detMC is well suited for fermionic systems at half filling. These methods fail for general fermionic problems because of the sign problem. In diagMC we explore the possibilities a sampling of the Feynman series (which has a sign problem that is not volume dependent) might offer for strongly correlated systems. In the DMFT approach we go in another direction: The system is solved selfconsistently for a small cluster while preserving information in Matsubara domain. If big enough clusters can be studied, the thermodynamic answer may be found after extrapolation in the cluster size.


Revealing the phase diagram of Kitaev materials by Machine Learning: Cooperation and Competition between spin Liquids

K. Liu, N. Sadoune, N. Rao, J. Greitemann, L. Pollet

Physical Review Research 3, 023016 (2021).

Show Abstract

Kitaev materials are promising materials for hosting quantum spin liquids and investigating the interplay of topological and symmetry-breaking phases. We use an unsupervised and interpretable machine-learning method, the tensorial-kernel support vector machine, to study the honeycomb Kitaev-Γ model in a magnetic field. Our machine learns the global classical phase diagram and the associated analytical order parameters, including several distinct spin liquids, two exotic S3 magnets, and two modulated S3×Z3 magnets. We find that the extension of Kitaev spin liquids and a field-induced suppression of magnetic order already occur in the large-S limit, implying that critical parts of the physics of Kitaev materials can be understood at the classical level. Moreover, the two S3×Z3 orders are induced by competition between Kitaev and Γ spin liquids and feature a different type of spin-lattice entangled modulation, which requires a matrix description instead of scalar phase factors. Our work provides a direct instance of a machine detecting new phases and paves the way towards the development of automated tools to explore unsolved problems in many-body physics.

DOI: 10.1103/PhysRevResearch.3.023016

Learning multiple order parameters with interpretable machines

K. Liu, J. Greitemann, and L. Pollet.

Physical Review B 99, 104410 (2019).

Show Abstract

Machine-learning techniques are evolving into a subsidiary tool for studying phase transitions in many-body systems. However, most studies are tied to situations involving only one phase transition and one order parameter. Systems that accommodate multiple phases of coexisting and competing orders, which are common in condensed matter physics, remain largely unexplored from a machine-learning perspective. In this paper, we investigate multiclassification of phases using support vector machines (SVMs) and apply a recently introduced kernel method for detecting hidden spin and orbital orders to learn multiple phases and their analytical order parameters. Our focus is on multipolar orders and their tensorial order parameters whose identification is difficult with traditional methods. The importance of interpretability is emphasized for physical applications of multiclassification. Furthermore, we discuss an intrinsic parameter of SVM, the bias, which allows for a special interpretation in the classification of phases, and its utility in diagnosing the existence of phase transitions. We show that it can be exploited as an efficient way to explore the topology of unknown phase diagrams where the supervision is entirely delegated to the machine.

DOI: 10.1103/PhysRevB.99.104410

Probing hidden spin order with interpretable machine learning

J. Greitemann, K. Liu, and L. Pollet.

Physical Review B 99, 060404(R) (2019).

Show Abstract

The search of unconventional magnetic and nonmagnetic states is a major topic in the study of frustrated magnetism. Canonical examples of those states include various spin liquids and spin nematics. However, discerning their existence and the correct characterization is usually challenging. Here we introduce a machine-learning protocol that can identify general nematic order and their order parameter from seemingly featureless spin configurations, thus providing comprehensive insight on the presence or absence of hidden orders. We demonstrate the capabilities of our method by extracting the analytical form of nematic order parameter tensors up to rank 6. This may prove useful in the search for novel spin states and for ruling out spurious spin liquid candidates.

DOI: 10.1103/PhysRevB.99.060404

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