Periodic Reporting for period 3 - HQMAT (New Horizons in Quantum Matter: From Critical Fluids to High Temperature Superconductivity) Reporting period: 2022-01-01 to 2023-06-30 Summary of the context and overall objectives of the project Understanding, controlling, and manipulating the flow of electrons in solid materials is perhaps the single most important scientific discovery that has shaped our modern world. One of the main goals of the field of condensed matter physics is to further advance the understanding of electronic properties of novel materials. This endeavor is interesting both from the point of view of fundamental physics, and due to its potential relevance to applications in the next generation of electronic devices. Systems of many interacting electrons pose a great theoretical challenge. These system display a rich interplay between quantum mechanics and many-body physics. The core of the Horizons in Quantum Matter (HQMAT) project deals with developing new approaches for analyzing strongly correlated quantum “liquids” made of electrons in solids, to predict their properties in different materials, and to propose new experiments that can probe these properties. To achieve this, we need to solve the quantum mechanical equations that describe the behavior of many electrons interacting with each other. This is, in general, a daunting task, and requires us to develop approximate models that capture the important physics yet are sufficiently simple to be tractable, and/or to resort to large-scale sophisticated numerical simulations. Specifically, our main goals in this project are:1. To develop a theory for quantum states of metals in the vicinity of an instability, known as “quantum critical metals”, which are believed to be the key for high temperature superconductivity. 2. To understand the behavior of correlated quantum electronic liquids where the interactions between particles are so strong such that the simple-minded approximation where electrons are treated as independent of each other breaks down. 3. To develop models that describe the behavior of novel correlated electronic systems, such as two-dimensional moire materials, and to predict new phenomena in these systems. Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far Some of the key results of the project are:- Theory of the strange metal Sr3Ru2O7 and related materials. Understanding “strange metals”, where the traditional theory describing electrons in metals breaks down, is one of the most important and long-standing open puzzles in condensed matter physics. The compound Sr3Ru2O7 is considered to a particularly clear example of such behavior. We have developed a theory for Sr3Ru2O7, which accounts for much of its puzzling behavior. This is a major step in developing a general understanding of strange metals. The theory has different unexpected consequences that are verified in experiments, and has led to various predictions in related materials that can now be tested experimentally. - Understanding of the hierarchy of energy scales associated with the approach to a quantum critical point in a metal. A metal tuned to the verge of an instability, such as a phase transition in which the metal becomes magnetic, is a rich and fascinating platform for exotic physics. In particular, it has often been found that such “quantum critical” metals become superconducting at relatively high temperatures. Despite its importance and apparent simplicity, theoretically understanding the properties of quantum criticality in metals has proven to be challenging. We have developed a method to simulate quantum critical metals using large-scale computers, which allows us to extract their properties without resorting to unjustified approximations. With this knowledge at hand, we have constructed a physical picture of the hierarchy of crossovers that the system undergoes upon approaching the quantum critical point, using analytical methods that are benchmarked against the numerical results. We believe that this is key advance in the field. - Numerically exact simulations for quantum critical metals in moire materials: One of the most exciting developments of the last years in condensed matter physics has been the discovery of strongly correlated phases of matter and superconductivity in twisted bilayer graphene. In this material, two graphene sheets are placed on top of one another with a small relative angle between them; the properties of the system are strikingly sensitive to the twist angle. In particular, at a special ‘magic’ value of the twist angle, the electronic dispersion becomes remarkably flat, enhancing the role of electron-electron interactions and leading to the aforementioned exotic phenomena. As is typical in strongly correlated electronic systems, there are very few theoretical techniques that can treat the physics of electrons in twisted bilayer graphene in a reliable manner. We have developed a new method for simulating twisted bilayer graphene at charge neutrality that includes the relevant degrees of freedom and resorts to as few approximations as possible, yet is tractable on present day computers. This approach may open a new window into the rich physics of this system, as well as serve as a benchmark to approximate theoretical methods. - Cascade of phase transitions and Pomeranchuk effect from strong correlations in twisted bilayer graphene. This part of our project involved a close collaboration with experimental groups, as part of the effort to understand the nature of the correlated liquid states that emerge in magic-angle twisted bilayer graphene (MATBG). This led to a set of discoveries that have fundamentally impacted the understanding of this system, and have become widely accepted and well cited in the community. In collaboration with S. Ilani’s group at Weizmann, we have constructed a simple model that explains the measurements of the electronic compressibility in MATBG in terms of a cascade of phase transitions where electrons of different spin and valley flavors are filled one by one upon changing the overall electronic density. We have then collaborated with the Ilani (WIS) and Young (UCSB) groups to reveal an electronic “Pomeranchuk effect” in MATBG, where an electronic liquid state of relatively low resistance undergoes a transition (or a rapid crossover) into a high-resistance state upon increasing temperature. The high resistance state is favored at high temperature because of its large excess electronic entropy, that arises from large fluctuations of an incipient spin/valley order parameter. This effect is analogous to the well-known Pomeranchuk effect in liquid helium 3, where the liquid state of helium atoms turns into a solid due to the higher spin entropy of the latter phase. We have collaborated with the experimentalists in understanding and modeling their results, as well as predicting the large excess entropy in the high resistance phase, that was indeed observed experimentally. This series of works was published in: Zondiner et al., Nature 582, 203 (2020); Saito et al., Nature 592, 220 (2021); Rozen et al., Nature 592, 214 (2021). This work was highlighted in an article in the online popular journal Physics World (https://physicsworld.com/a/electrons-in-twisted-graphene-freeze-when-heated/) and was also featured in an article in the front page of Haaretz.co.il one of the leading newspapers in Israel. Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far) 1. Predicting new behaviors of quantum critical metals in parameters regimes that have not been explored before, offering a new interpretation of ongoing experiments in quantum materials. 2. Formulating theoretical principles for strange metal behavior and applying these to new material systems. 3. Extensive simulations of twisted bilayer graphene using our new numerical method, contributing to the understanding of this system and predicting new physical effects. 4. Developing the theory for novel superconductivity in two-dimensional correlated materials, and predicting its experimental consequences.