Quantum Matter

Research Areas

The work of the Quantum Matter group spans several cutting-edge topics in condensed matter physics, with an emphasis on quantum magnetism, disorder, and strongly correlated systems. These systems are characterized by the intricate interplay between quantum mechanics and many-body interactions, leading to highly non-trivial ground states and low-temperature phases. Some key research areas are listed below.

• Quantum magnetism and frustration
  The group studies magnetic systems where the interactions between spins lead to competing tendencies, resulting in frustrated configurations that prevent the system from settling into a conventional magnetic order, leading to novel quantum states, including spin liquids where long-range magnetic order is absent even at absolute zero temperature.

• Strongly correlated quantum systems
  In materials with strong electron-electron interaction, e.g., cuprates, organic conductors, iron pnictides, etc., classical descriptions break down, giving rise to phenomena such as unconventional superconductivity or magnetic textures. Moreover, the role of quantum fluctuations is very pronounced in one-dimensional correlated quantum systems, where advanced analytic and numerical techniques are needed to go beyond mean-field theories. The group also develops new methodological frameworks and employs embedding techniques that capture strong local electronic correlations while preserving a realistic description of the material as a whole.

• Topological phases
  The group is also active in the study of topologically-ordered systems and symmetry-protected topological phases, where quantum phases are distinguished not by local order parameters but by global topological invariants. This area is crucial for understanding quantum computing and topological quantum computing.

• Disorder and Many-Body Localization
  A key area of the group’s work is the study of disordered quantum systems, especially in the context of many-body localization. This is a fascinating phenomenon in which disorder can prevent thermalization in an interacting quantum system, leading to non-ergodic behavior and the persistence of quantum coherence at infinite times.
• One-dimensional quantum systems
  Our research group explores the unique physics of one-dimensional quantum systems, where strong confinement forces particles to move along a single line. In this restricted geometry, the familiar rules of three-dimensional physics break down; particles cannot simply bypass one another, leading to highly collective behaviors and strong quantum correlations. Using both theoretical modeling and computational tools, we study these phenomena across platforms such as ultra-cold quantum gases or quantum wires.

Methods

The group members use combinations of analytical techniques and state-of-the-art numerical methods to study these systems. Analytical approaches include effective field theories, renormalization group techniques, and Bethe ansatz. They provide a conceptual framework for understanding low-energy excitations, phase transitions in quantum materials, as well as a way to obtain exact results for certain models. Numerically, the group is skilled in exact diagonalization, quantum Monte Carlo simulations, tensor network approaches, and density matrix renormalization group. The group also develops ab initio electronic structure methods to study real materials. These methods avoid the explicit use of the many-body wavefunction to compute the observables of interest. Instead, they rely on simpler reduced quantities, such as the electronic density, the one-body density matrix, and the N-body Green’s function. In particular, theoretical formalisms based on Green’s functions are especially powerful because they directly provide access to spectroscopic observables, such as photoemission and optical absorption spectra, which are central to the group’s research.