Theoretical Solid State Physics

Ludwig-Maximilians-Universität München

Theoretical Solid State Physics

Theresienstr. 37

80333 Munich

Tel. +49 89 2180 4539


Research Group


Research focus: mathematical physics, effective theories, quantum electrodynamics

The research in our group is focused on properties of strongly correlated quantum matter. A thorough theoretical understanding of such systems is a necessary prerequisite for the development of new materials, which will likely build the foundation of future quantum technologies. Our aim is to identify, characterize and classify interesting and novel quantum phases of matter in paradigmatic examples of strongly correlated electron materials, such as high-Tc cuprate superconductors and frustrated antiferromagnets, as well as ultracold atomic gases.

High Temperature Superconductors

Understanding the properties of high-Tc cuprate superconductors in the pseudo-gap regime remains one of the outstanding questions in the field of strongly correlated electron systems. Recent measurements show that in-plane electronic transport in the pseudo-gap regime is plain-vanilla Fermi-liquid like, whereas several other experimental probes clearly demonstrate a drastic reduction of available electronic states close to the Fermi energy. One promising approach to explain these results is to assume that the ground-state of the is a so-called fractionalized Fermi liquid (FL*). This exotic state of matter has been proposed at first to understand properties of heavy-Fermion materials, where the relevant physical properties arise due to the interaction between a band of conduction electrons and localized f-electrons. Recently we developed a simple single band, which seems to capture several key properties of the metal.

[1]. One of our goals in the near future is to study this in detail.

[1] M. Punk, A. Allais, and S. Sachdev, "A quantum dimer model for the pseudogap metal", arxiv: 1501.00978


Magnets with frustrated exchange interactions provide an ideal playground to study exotic quantum phases of matter. These systems can exhibit so-called quantum spin-liquid ground states, which display a variety of interesting physical phenomena such as fractionalized excitations and topological order. Several candidate materials which may host such quantum spin-liquid phases have been identified in recent years, but many theoretical aspects of spin-liquids are still poorly understood. For example, simple mean-field models for such phases often exist, but in many cases they do not capture essential features that are observed in experiments [2]. Trying to span the bridge between experiments and exotic theoretical models is one of our main motivations to work in this field.

[2] M. Punk, D. Chowdhury, and S. Sachdev, “Topological excitations and the dynamic structure factor of spin-liquids on the kagome lattice”, Nature Physics 10, 289-293 (2014)


From Luttinger liquids to Luttinger droplets via higher-order bosonization identities

S. Huber, M.2 Kollar

Physical Review Research 2, 043336 (2020).

Show Abstract

We derive generalized Kronig identities expressing quadratic fermionic terms including momentum transfer to bosonic operators and use them to obtain the exact solution for one-dimensional fermionic models with linear dispersion in the presence of position-dependent local interactions and scattering potential. In these Luttinger droplets, which correspond to Luttinger liquids with spatial variations or constraints, the position dependencies of the couplings break the translational invariance of correlation functions and modify the Luttinger-liquid interrelations between excitation velocities.

DOI: 10.1103/PhysRevResearch.2.043336

Slave-boson description of pseudogap metals in t-J models

J. Brunkert, M. Punk

Physical Review Research 2, 043019 (2020).

Show Abstract

We present a simple modification of the standard U(1) slave boson construction for the single band t-J model which accounts for two-particle bound states of spinons and holons. This construction naturally gives rise to fractionalized Fermi-liquid ground states, featuring small, hole-like pocket Fermi surfaces with an anisotropic quasiparticle weight in the absence of broken symmetries. In a specific parameter regime our approach maps the square lattice t-J model to a generalized quantum dimer model, which was introduced as a toy model for the metallic pseudogap phase in hole-doped cuprates in [Proc. Natl. Acad. Sci. USA 112, 9552 (2015)]. Our slave boson construction captures essential features of the nodal-antinodal dichotomy and straightforwardly describes sharp, Fermi arc-like features in the electron spectral function. Moreover, it allows us to study quantum phase transitions between fractionalized Fermi-liquid phases and superconductors or ordinary Fermi liquids.

DOI: 10.1103/PhysRevResearch.2.043019

Solvable lattice models for metals with Z2 topological order

B. Verheijden, Y. Zhao, M. Punk

Scipost Physics 7 (6), 074 (2019).

Show Abstract

We present quantum dimer models in two dimensions which realize metallic ground states with Z2 topological order. Our models are generalizations of a dimer model introduced in [PNAS 112, 9552-9557 (2015)] to provide an effective description of unconventional metallic states in hole-doped Mott insulators. We construct exact ground state wave functions in a specific parameter regime and show that the ground state realizes a fractionalized Fermi liquid. Due to the presence of Z2 topological order the Luttinger count is modified and the volume enclosed by the Fermi surface is proportional to the density of doped holes away from half filling. We also comment on possible applications to magic-angle twisted bilayer graphene.

doi: 10.21468/SciPostPhys.7.6.074

Incommensurate 2k(F) density wave quantum criticality in two-dimensional metals

J. Halblinger, D. Pimenov, M. Punk

Physical Review B 99 (19), 195102 (2019).

Show Abstract

We revisit the problem of two-dimensional metals in the vicinity of a quantum phase transition to incommensurate Q = 2k(F) charge-density-wave order, where the order-parameter wave vector Q connects two hot spots on the Fermi surface with parallel tangents. Earlier theoretical works argued that such critical points are potentially unstable, if the Fermi surface at the hot spots is not sufficiently flat. Here we perform a controlled, perturbative renormalization-group analysis and find a stable fixed point corresponding to a continuous quantum phase transition, which exhibits a strong dynamical nesting of the Fermi surface at the hot spots. We derive scaling forms of correlation functions at the critical point and discuss potential implications for experiments with transition-metal dichalcogenides and rare-earth tellurides.

DOI: 10.1103/PhysRevB.99.195102

Accept privacy?

Scroll to top