# Research Fields

- Strongly correlated electrons and novel phases
- Quantum phase transitions
- Frustrated magnets and spin liquids
- Topological phases (insulators, superconductors, magnets)
- High-temperature superconductors
- Heavy-fermion metals
- Cold atoms in optical lattices
- Quantum impurity problems
- Dissipative quantum systems

## Recent Highlights

**Emergence of mesoscale quantum phase transitions in a ferromagnet**

LiHoF_{4} is a textbook example for a material displaying a transverse-field Ising quantum phase transition. We have studied its behavior for applied fields tilted away from the direction transverse to the easy axis and found - surprisingly - a line of sharp phase transitions at low temperatures, in contrast to the crossover expected from microscopic theory. These transition involve the appearance or disappearance of magnetic domains and hence are of mesoscopic character. Our detailed modelling is in excellent agreement with experimental data.

A. Wendl, H. Eisenlohr, F. Rucker, C. Duvinage, M. Kleinhans, M. Vojta, and C. Pfleiderer, Nature **609**, 65 (2022) (Nature)(arXiv)

**Exotic quantum phase transitions in Dirac semimetals**

Fermion interactions in Dirac semimetals can lead to a variety of ordering phenomena. We have studied different microscopic models which admit (i) phases with electron-nematic order and (ii) phases which break a built-in SO(3)xU(1) symmetry. Using field theory and quantum Monte-Carlo simulations, we were able to fully characterize the resulting quantum phase transition. Among the findings is a novel instance of deconfined quantum criticality.

- J. Schwab, L. Janssen, K. Sun, Z. Y. Meng, I. F. Herbut, M. Vojta, and F. F. Assaad, Phys. Rev. Lett.
**128**, 157203 (2022) (Phys. Rev. Lett.)(arXiv) - Z. H. Liu, M. Vojta, F. F. Assaad, and L. Janssen, Phys. Rev. Lett.
**128**, 087201 (2022) (Phys. Rev. Lett.)(arXiv)

**Kondo breakdown in a spin chain on a semimetal**

The Kondo effect describes the screening of magnetic moments in metals. Its breakdown can lead to unconventional phase transitions and exotic phases. We have studied the physics of a spin chain coupled to a two-dimensional Dirac semimetal. This system shown a non-trivial quantum phase transition where the Kondo effect breaks down. These results are relevant for instance for magnetic adatoms on graphene.

- B. Danu, M. Vojta, F. F. Assaad, and T. Grover, Phys. Rev. Lett.
**125**, 206602 (2020) (Phys. Rev. Lett.)(arXiv)

**Magnon Landau levels in strained antiferromagnets**

Strain has become an important tool to engineer novel states of matter. In particular, inhomogeneous strain applied to lattice systems can induce artificial gauge fields for particles moving on this lattice. We have demonstrated how to engineer a novel state in Mott-insulating magnets, namely an antiferromagnet with a Landau-level excitation spectrum of magnons.

- M. M. Nayga, S. Rachel, and M. Vojta, Phys. Rev. Lett.
**123**, 207204 (2019) ( Phys. Rev. Lett.), (arXiv)

**Local Mott quantum criticality in the Hubbard model**

The interaction-driven Mott metal-Insulator transition is one of the most important phenomena of strongly correlated electrons. Searching for quantum criticality in the framework of dynamical mean-field theory for the one-band Hubbard model, we have found a scale-invariant, i.e. critical, isolating state at T=0 whose finite-temperature dynamics controls quantum-critical behavior in both the single-particle spectrum and the electrical resistivity.

- H. Eisenlohr, S.-S. B. Lee, M. Vojta, Phys Rev. B
**100**, 155152 (2019) (Phys. Rev. B) (arXiv)

**Cluster spin-glass phase in disordered pyrochlore magnets**

Magnets with pyrochlore lattice structure form one of the most interesting families of geometrically frustrated magnets. In the presence of an XY anisotropy, they realize order states via a fluctuation-driven order-by-disorder mechanism. We have studied the effect of quenched disorder (i.e. lattice defects) and found a novel spin-glass phase, thus explaining existing experiments.

- E. C. Andrade, J. A. Hoyos, S. Rachel, and M. Vojta, Phys. Rev. Lett.
**120**, 097204 (2018) (Phys. Rev. Lett.)(arXiv)

**Heisenberg-Kitaev model in a magnetic field**

The Heisenberg-Kitaev model, discussed for materials like Na_{2}IrO_{3} oder alpha-RuCl_{3}, describes spin systems with so-called compass interactions on the honeycomb lattice. We have systematically studied the effect of an external magnetic field and determined phase diagrams for different field directions. For <111> fields we find a number of non-trivial phases, including multi-Q states and vortex crystals.

- L. Janssen, E. C. Andrade, and M. Vojta, Phys. Rev. Lett.
**117**, 277202 (2016) (Phys. Rev. Lett.) (arXiv)

**Strain-induced Landau Levels in arbitrary dimensions with an exact spectrum**

Free electrons in two space dimensions subject to a magnetic field realize Landau levels, highly degenerate states which form the basis of the quantum Hall effect. Artificial approximate Landau levels can be induced by suitable lattice deformations also in the absence of a magnetic field. We have introduced and solved a family of models for strained bipartite lattices which yield perfectly quantized Landau levels in arbitrary space dimensions.

- S. Rachel, I. Göthel, D. P. Arovas, and M. Vojta, Phys. Rev. Lett.
**117**, 266801 (2016) (Phys. Rev. Lett.) (arXiv)

**Kondo effect in quasicrystals**

The Kondo effect describes the screening of a magnetic impurity embedded into a metallic host - the latter is typically a crystal with a periodic arrangement of atoms. We have theoretically investigated, for the first time, the Kondo effect in quasicrystalline metal. A quasicrystal is a solid in which atoms are arranged in a non-periodic fashion. Our results show strong spatial fluctuations of screening, leading to a broad distribution of Kondo temperatures which eventually causes non-Fermi liquid behavior.

- E. C. Andrade, A. Jagannathan, E. Miranda, M. Vojta, and V. Dobrosavljevic, Phys. Rev. Lett.
**115**, 036403 (2015) (Phys. Rev. Lett.) (arXiv)

**Systematic expansion for quantum critical magnets**

Quantum magnets built from pairs of coupled spins display interesting quantum phase transitions. We have developed a novel non-linear bond-operator theory which enables a analytic description of such systems in a systematic expansion in 1/*d* where *d* is the number of spatial dimensions.

- D. G. Joshi and M. Vojta, Phys. Rev. B
**91**, 094405 (2015) (Phys. Rev. B) (arXiv) - D. G. Joshi, K. Coester, K. P Schmidt, and M. Vojta, Phys. Rev. B
**91**, 094404 (2015) (Phys. Rev. B) (arXiv)

**Dynamics of spontaneous symmetry breaking**

Ordered states of matter are typically characterized by spontananeously broken symmetries. We have investigated the *dynamics* of spontaneous symmetry breaking: How can a quantum system evolve from a symmetric initial state into a symmetry-broken final state? For a minimal model, the ferromagnetic Kondo model, we have shown that an infinitesimal field is sufficient to induce a finite order parameter in the long-time limit.

- M. Heyl and M. Vojta, Phys. Rev. Lett.
**113**, 180601 (2014) (Phys. Rev. Lett.) (arXiv)