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A central problem in modern condensed matter physics is the understanding of materials with strong electron correlations. Despite extensive work, the essential physics of many of these systems is not understood and there is very little ability to make predictions in this class of materials. In this manuscript we share our personal views on the major open problems in the field of correlated electron systems. We discuss some possible routes to make progress in this rich and fascinating field. This manuscript is the result of the vigorous discussions and deliberations that took place at Johns Hopkins University during a three-day workshop January 27, 28, and 29, 2020 that brought together six senior scientists and 46 more junior scientists. Our hope, is that the topics we have presented will provide inspiration for others working in this field and motivation for the idea that significant progress can be made on very hard problems if we focus our collective energies. 

Abstract The origin of the weak insulating behavior of the resistivity, i.e. $${\rho }_{xx}\propto {\mathrm{ln}}\,(1/T)$$ ρ x x ∝ ln ( 1 / T ) , revealed when magnetic fields ( H ) suppress superconductivity in underdoped cuprates has been a longtime mystery. Surprisingly, the high-field behavior of the resistivity observed recently in charge- and spin-stripe-ordered La-214 cuprates suggests a metallic, as opposed to insulating, high-field normal state. Here we report the vanishing of the Hall coefficient in this field-revealed normal state for all $$T\ <\ (2-6){T}_{{\rm{c}}}^{0}$$ T < ( 2 − 6 ) T c 0 , where $${T}_{{\rm{c}}}^{0}$$ T c 0 is the zero-field superconducting transition temperature. Our measurements demonstrate that this is a robust fundamental property of the normal state of cuprates with intertwined orders, exhibited in the previously unexplored regime of T and H . The behavior of the high-field Hall coefficient is fundamentally different from that in other cuprates such as YBa 2 Cu 3 O 6+ x and YBa 2 Cu 4 O 8 , and may imply an approximate particle-hole symmetry that is unique to stripe-ordered cuprates. Our results highlight the important role of the competing orders in determining the normal state of cuprates. 

The phase diagram of underdoped cuprates in a magnetic field ( H ) is key to understanding the anomalous normal state of these high-temperature superconductors. However, the upper critical field ( H c2 ), the extent of superconducting (SC) phase with vortices, and the role of charge orders at high H remain controversial. Here we study stripe-ordered La-214, i.e., cuprates in which charge orders are most pronounced and zero-field SC transition temperatures T c 0 are lowest. This enables us to explore the vortex phases in a previously inaccessible energy scale window. By combining linear and nonlinear transport techniques sensitive to vortex matter, we determine the T − H phase diagram, directly detect H c2 , and reveal novel properties of the high-field ground state. Our results demonstrate that quantum fluctuations and disorder play a key role as T → 0 , while the high-field ground state is likely a metal, not an insulator, due to the presence of stripes.