This award supports theoretical research and education to study fractionalized phases in spin, boson, and electron systems in 2D that have many low-energy itinerant excitations. This research is motivated by experiments on several recently discovered candidate spin-liquid materials, and from observations of non-Fermi-liquid itinerant electron states in strongly correlated materials such as the strange metal and pseudogap phases in the cuprate high temperature superconductors. The field of quantum magnetism has experienced a new era stimulated by the cuprates and by many studies of magnetic insulators with competing interactions. Quantum spin systems are prototypical examples of many-body physics; one of the conceptual developments is the possibility of spin liquid phases. A recent breakthrough is the appearance of several candidate experimental realizations which appear to be gapless spin liquids where theory is less established. A proposed state for two triangular lattice spin liquid materials has a Fermi surface of spinons, which is a kind of ?spin metal". The PI aims to determine how well these materials can be understood within the available theoretical frameworks. Having learned about such unusual states in the magnetism context, the PI will apply these ideas to understand itinerant non-Fermi-liquids of electrons. In the cuprate context, one can ask whether charge degrees of freedom can be put back into play and study the strange metal. Focusing on the itinerant charge sector, and slave-particle approaches borrowed from spin-liquid studies enable the construction of non-perturbative charge liquids. ?Bose metals.? The PI will pursue the next step, a similar program for electronic systems bringing together spin and charge sectors. An important thrust of this research is to search for such ?spin metals," ?Bose metals," and electronic non-Fermi-liquids in model systems and guide numerical studies. A promising approach is to build up towards 2D using controlled DMRG studies of candidate models on quasi-1D ladders combined with trial wavefunctions and gauge theory/bosonization analysis. The PI will also study phase transitions in statistical mechanics models with matter fields coupled to gauge fields in 2+1D. These arise as effective field theories for recently proposed unconventional quantum critical points between competing phases in quantum magnets. Establishing the nature of the transitions in such gauge theories will put further theoretical developments on firmer ground. The PI will also study phases and phase transitions in models with statistical interactions.
NON-TECHNICAL SUMMARY This award supports theoretical research and education that aims to discover new magnetic states of matter, to understand their implications for unusual metallic states that appear in high temperature superconductors, and to understand exotic transformations that can occur among them that lie outside the standard theory of phase transitions. This research is motivated and stimulated by the discovery of new materials with unusual properties that challenge conventional paradigms of condensed matter physics. The emphasis of this research will be on developing theoretical concepts in the context of laboratory and computer experiments on materials and models.
This is fundamental research that contributes to the intellectual foundations of our understanding of materials and new states of matter that exhibit properties and exotic phenomena that lie outside our current understanding. This is an intellectual pursuit in its own right no less fascinating than the study of the universe, but it may also lead to the discovery of new phenomena and to new device technologies.
We understand very well conventional metals like copper or silver, which was achieved already in the early days of quantum mechanics by treating electrons as essentially non-interacting fermions. In fact, much of the modern electronics relies on our ability to predict and control conducting properties of metals and semi-conductors. On the other hand, high-temperature cuprate superconductors discovered twenty five years ago apparently have conducting phases that defy the conventional theory of metals -- so-called Landau's theory of Fermi liquids. Understanding these unusual metals may also shed light on the origin of the high-temperature superconductivity. However, progress in this direction has been hampered by lack of any controlled theoretical examples realizing non-Fermi liquids. Much of the work supported by this grant and done in collaboration with researches at UCSB and Cal-State Northridge has been building up to achieve such examples. One of the main steps in our program is construction of metallic phases of bosons at zero temperature. We pursued a particular theoretical route towards such "Bose metals" where we imagine splintering bosons into itinerant fermionic partons. We vigorously studied candidate frustrated spin and boson models with ring exchanges to realize such phases. The spin models are relevant for the recently discovered spin liquids in several layered (essentially two-dimensional) organic antiferro-magnetic materials, which do not show any signs of magnetic order and have unusual metal-like thermal properties despite being electrical insulators. While the study directly in two dimensions is very challenging, we made significant progress bolstering the argument for a spin variant of Bose-metal by considering ladder systems using numerical and analytical techniques, and we also explored many experimentally relevant questions in this controlled quasi-one-dimensional setting. We pursued similar program for bosons at generic densities and established existence of Bose-metals on ladders, as well as in special limiting cases directly in two dimensions. Very recently, we attacked the problem of electronic non-Fermi liquids by proposing a state where we splinter electrons into bosonic chargons and fermionic spinons and further require the chargons to be in the charge Bose-metal state while spinons are in the Spin Bose-metal state, thus bringing together the separate charge and spin building blocks to construct exotic electronic metal. We proposed a concrete electronic model with ring exchanges and established the presence of such a non-Fermi liquid on a two-leg ladder. This is the first example of a conducting phase with gapless electrons that does not fit into the Fermi liquid paradigm, thus raising our hopes to tackle this challenging problem. Besides the non-Fermi-liquid metals, this grant also initiated studies of phases and phase transitions in systems where we have particles with unusual statistics. Presence of such quasi-particles (excitations) is one of the hallmarks of topological quantum phases. We can understand possible proximate phases and phase transitions by studying what happens when such particles want to proliferate. Carrying out such a program is challenging since the unusual statistics implies quantum interferences that confound our intuition. We explored a particular example in 2+1 space-time dimensions with two species of particles that are bosons by themselves but have mutual statistics characterized by a statistical angle theta. We examined in detail representative cases of theta and provided complete understanding of the rich phase diagrams by a combination of numerical Monte Carlo and analytical duality methods. This work has potential to stimulate other lattice realizations of topological theories allowing precise and unbiased studies of these.
