Characterizing the properties of quantum materials and their different quantum phases is paramount in order to be able to develop new alternative technologies beyond the semiconductor paradigm for applications in energy conversion, electronic devices, and light harvesting. This award supports research and education that will not only have technological implications but will also tackle fundamental questions in physics that could lead to unanticipated discoveries.
The quest for materials with novel functionality is driven by the study of quantum systems where interactions among the constituent electrons are very strong. These interactions can give rise to complex and intriguing phenomena that take place when the physics is mostly governed by the collective behavior of the electrons inside the material. One particular example occurs when considering electrons confined in low spatial dimensions: the confinement forces electrons to move by "pushing" instead of passing around each other. Same as oscillations of a string, the natural excitations of such a confined system of electrons can be better understood in terms of waves. As a consequence, electrons lose their individual identities as particles. This project focuses on understanding how electrons lose or recover their identities as individual excitations and how their behavior is subsequently transformed, giving rise to different phases in the material.
Even though these problems are theoretically very challenging due to their underlying complexity, they are amenable to numerical methods. The focus of the research is computational in nature and will also involve the development of new innovative algorithms based on quantum information and machine-learning ideas. New tools for scientific discovery will be developed and will be made available to the community as open-source software that may find applications in other disciplines beyond condensed matter physics.
This award will support research and education focused on tackling urgent questions concerning different instabilities in strongly correlated materials due to the presence of antiferromagnetic long-range order and van Hove singularities. This project tackles a paradigmatic problem in condensed matter from a new perspective. In order to overcome the limitations of the Mermin-Wagner theorem, chains and ladders will be studied in the presence of long-range interactions that can realize actual spontaneous symmetry breaking and true antiferromagnetic order. The research will address questions of a very fundamental nature: i) How do spinons evolve into magnons and what are their signatures in the excitation spectrum? ii) Is it possible to realize fractionalized excitations and coherent excitations simultaneously in different regions of the Brillouin zone? iii) How do coherent quasiparticles form (if at all), in the presence of long-range order? Will we still observe signatures of spin-charge separation in the spectrum? iv) What is the interplay between long-range antiferromagnetic order and pairing? v) What terms in the Hamiltonian would give rise to competing instabilities such as those observed in superconducting cuprates? The method of choice will be the density matrix renormalization group and its time-dependent variants, which were co-developed by the PI and have had a remarkable success expanding our knowledge of correlation effects to the time domain.
This work is complemented by the development of novel computational approaches to tackle higher-dimensional systems based on new original ideas that bridge quantum information and machine learning: i) The use of lapped orthogonal orbitals that interpolate between real- and momentum-space representations, ii) Quantum disentanglers and natural orbitals to construct the wave functions of the elementary quasiparticle excitations, and iii) Using restricted Boltzmann machines to calculate the single-particle Green's functions, and therefore reconstruct the entire excitation spectrum of the quantum many-body problem. These new tools will be made available to the community as open-source software that may find applications in other disciplines beyond condensed matter physics.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
