## Quantum and Topological Matter meeting

**01Nov2019**13:00 - 18:00

Speakers: Mark-Oliver Goerbig (Université Paris Sud), Vadim Cheianov (Leiden University), Dmytro Makogon (Utrecht University, and Natalia Chepiga (University of Amsterdam). Location: Utrecht.

### Programme

**13:15-14:00 Mark-Oliver Goerbig (Université Paris Sud)** - *Unveiling the Berry curvature in the spectral properties in 2D transition-metal dichalcogenides*

**14:00-14:45 Vadim Cheianov (Leiden University)** - *Symmetry-restoring quantum phase transition in a two-dimensional spinor condensate *

**15:15-16:00 Dmytro Makogon (Utrecht University, currently ABN AMRO)**-** ***Median-point approximation and its application for the study of fermionic system *

**16:00-16:45 Natalia Chepiga (University of Amsterdam)**, *A comb tensor network*

**16:45 borrel (drinks)**

### Abstracts

**Mark-Oliver Goerbig (Université Paris Sud) **

*Unveiling the Berry curvature in the spectral properties in 2D transition-metal dichalcogenides*

Abstract: The Berry curvature as a relevant geometric quantity in the characterisation of electronic bands in solids is a key concept in the understanding of the topological properties of condensed matter ever since the advent of graphene and topological insulators in 2005 and 2006. However, the concept had been known before but left aside as a curiosity of the quantum-mechanical properties of electrons in solids. This lack of interest in the Berry curvature is most probably due to the absence of its manifestation in the spectral properties of electrons in solids, within conventional band theory. Indeed, in order to uncover its relevance, (local) electric fields are required, as it is evident when considering the quasi-classical equations of motion of band electrons in the form of the anomalous velocity of Karplus and Luttinger. However, this does not mean that the Berry curvature is absent in all spectral properties. Indeed, it was observed some years ago that excitons in a novel class of semiconducting two-dimensional materials (transition-metal dichalcogenides) do not obey they otherwise extremely successful hydrogen model used in the description of excitons. While non-local screening effects, due to the layered structure of the material, is certainly one reason for the observed deviations, a conceptually more important effect is precisely the role played by the Berry curvature that is non-zero at the direct gap at the K and K' points in the first Brillouin zone. The electric field, which arises from the mutual Coulomb attraction between the electron and the hole that build up the exciton, is precisely the quantity that couples to the (excitonic) Berry curvature, and additional terms arise in the fundamental Hamiltonian, which determines the dynamical and thus spectral properties of the excitons.

[1] M. Trushin et al., Phys. Rev. B 94, 041301(R) (2016).

[2] M. Trushin et al., Phys. Rev. Lett. 120, 187401 (2018).

[3] A. Hichri et al., Phys. Rev. B 100, 115426 (2019).

**Vadim Cheianov (Leiden University) **

*Symmetry-restoring quantum phase transition in a two-dimensional spinor condensate*

Abstract: Bose Einstein condensates of spin-1 atoms are known to exist in two different phases, both having spontaneously broken spin-rotation symmetry, a ferromagnetic and a polar condensate. Here we show that in two spatial dimensions it is possible to achieve a quantum phase transition from a polar condensate into a singlet phase symmetric under rotations in spin space. This can be done by using particle density as a tuning parameter. Starting from the polar phase at high density the system can be tuned into a strong-coupling intermediate-density point where the phase transition into a symmetric phase takes place. By further reducing the particle density the symmetric phase can be continuously deformed into a Bose-Einstein condensate of singlet atomic pairs. We calculate the region of the parameter space where such a molecular phase is stable against collapse

**Dmytro Makogon (Utrecht University, currently ABN AMRO)**

*Median-point approximation and its application for the study of fermionic system *

Abstract: We introduce a novel median-point approximation method as an extension of the Laplace's (saddle-point approximation) method and illustrate it with applications for real scalar functions. Furthermore, we consider a system of fermions with local interactions on a lattice and apply a multivariate generalization of the method for evaluation of the corresponding partition function, aiming at investigating the possibility of a superconducting second-order phase transition.

**Natalia Chepiga (University of Amsterdam)**

*A comb tensor network*

Abstract: I will talk about special kind of tree tensor networks that has geometry of a comb. Together with S. R. White we have developed an efficient variational optimization of the wave-function in the comb geometry and compare its complexity with one of the density matrix renormalization group (DMRG) algorithm. I will discuss three applications of the algorithm. In Heisenberg spin-1 comb, edge states localized at the end of the Haldane teeth form a critical spin-1/2 chain, the position of which depends on a backbone coupling constant. Also, we detect an emergence of "higher-order" edge states in the corners a comb lattice. In spin-1/2 Heisenberg model on a comb lattice we observe a competition between critical behavior in two orthogonal directions that affect a conformal invariance of the system. Finally, I will discuss Ising comb in a transverse field that exhibits a first order transition on any finite-size cluster due to special type of edge states and which is expected to turn into a continuous transition in the thermodynamic limit.

### Location

Marinus Ruppert building, room Rood ['red'], adress: Leuvenlaan 1, Utrecht

### Local organiser

Lars Fritz (UU)

l.fritz [at] uu.nl

### About

This event is part of a regular series of meetings on Quantum and Topological Matter, sponsored by Delta ITP, with the objective of bringing together the theoretical physics communities in Amsterdam, Leiden, Utrecht.