Condensed Matter

We study the possibility of a deconfined quantum phase transition in a realistic model of a two dimensional Shastry-Sutherland quantum magnet, using both numerical and field theoretic techniques. We argue that the quantum phase transition between a two fold degenerate plaquette valence bond  solid (pVBS) order and N\'eel ordered phase may be described by a deconfined quantum critical point (DQCP) with emergent O(4) symmetry. Further, using the infinite density matrix renormalization group (iDMRG) numerical technique, we verify the emergence of an intermediate pVBS order, between the dimer and Neel ordered phases. By analyzing the correlation length spectrum, we provide evidence for deconfinement and emergent O(4) symmetry at the phases transistion between the pVBS and N\'eel orders. Such a phase transition has been reported in the recent pressure tuned experiments in the Shastry-Sutherland lattice material  SrCu2(BO3)2. The non-symmorphic lattice structure of the Shastry-Sutherland compound leads to extinction points in the scattering, where we predict sharp signatures of a DQCP in both the phonon and magnon spectra associated with the spinon continuua. Our results can guide future experimental studies of DQCP in quantum magnets.

The construction of soluble lattice toy models is an important theoretical approach in the study of strongly interacting topological phases of matter. On the other hand, the primary experimental probe to such systems is via electromagnetic response. Somewhat unsatisfactorily, the current systematic construction of the lattice toy models focuses on braiding statistics and does not admit coupling to an electromagnetic background. Thus there is a mismatch between our theoretical approach and experimental probe. In this talk I introduce how to systematically incorporate electromagnetic response into the soluble lattice toy models, for a large class of abelian topological phases. [Reference: 1902.06756] 

Experiments with ultracold fermionic gases are thriving and continue to provide us with valuable insights into fundamental aspects of physics. A special system of interest is the so-called unitary Fermi gas (UFG) situated right in the "middle" of the crossover between Bardeen-Cooper-Schrieffer superfluidity and Bose-Einstein condensation. However, the theoretical treatment of these gases is highly challenging due to the absence of a small expansion parameter as well as the appearance of the infamous sign problem in the presence of, e.g., finite spin polarizations. In this talk, I will discuss the concept of stochastic quantization and motivate the complex Langevin (CL) method for non-relativistic fermions as an alternative to conventional Monte Carlo approaches. In particular, I will show how the CL approach can be employed to study the spin-polarized UFG. In the unpolarized limit, our results for the EOS are in excellent agreement with the existing state-of-the-art results from other ab-initio approaches as well as with experimental data. For the polarized case, our results for the EOS and other thermodynamic quantities represent experimentally testable predictions, already providing us with some insight into the underlying phase diagram.

In crystals, quantum electrons can be spatially distributed in a way that the bulk solid supports macroscopic electric multipole moments, which are deeply 

related with emergence of topology insulators in condensed matter systems. However, unlike the classical electric multipoles in open space, 

defining electric multipoles in crystals is a non-trivial task. So far, only the dipolar moment, namely polarization, has been successfully defined and served as a classic example of topological insulators. 

In this talk, we propose the general definition, i.e., many-body invariants, for electric multipoles in crystals, which are related with recently-discovererd higher-order topological insulators. 

Our invariants are designed to measure the distribution of electron charge in unit cells and thus can detect multipole moments purely from the bulk ground state wavefunctions. 

We provide analytic as well as numerical proofs for our invariants. Application of our invariants to spin systems as well as various other aspects of the many-body invariants will be briefly discussed.