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Coherent driving has established itself as a powerful tool for guiding a many-body quantum system into a desirable, correlated pre-thermal regime. The focus on this transient regime where heating is slow is a result of the intuition that a thermodynamically large system will inevitably saturate to a featureless infinite temperature state under continuous driving. Here we show that whether or not Floquet heating is a deleterious effect actually depends on the geometry of the system. Specifically, we prove that the maximum entropy steady states which form upon driving the ground state of the Hubbard model on unbalanced bi-partite lattices possess uniform off-diagonal long-range order which remains finite even in the thermodynamic limit. This creation of a `hot condensate can occur on any driven unbalanced lattice and provides an understanding of how heating can expose order which has been suppressed by the lattice geometry. We discuss implications for recent experiments observing emergent superconductivity in photoexcited materials.
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The noninteracting electronic structures of tight binding models on bipartite lattices with unequal numbers of sites in the two sublattices have a number of unique features, including the presence of spatially localized eigenstates and flat bands. When a emph{uniform} on-site Hubbard interaction $U$ is turned on, Lieb proved rigorously that at half filling ($rho=1$) the ground state has a non-zero spin. In this paper we consider a `CuO$_2$ lattice (also known as `Lieb lattice, or as a decorated square lattice), in which `$d$-orbitals occupy the vertices of the squares, while `$p$-orbitals lie halfway between two $d$-orbitals. We use exact Determinant Quantum Monte Carlo (DQMC) simulations to quantify the nature of magnetic order through the behavior of correlation functions and sublattice magnetizations in the different orbitals as a function of $U$ and temperature. We study both the homogeneous (H) case, $U_d= U_p$, originally considered by Lieb, and the inhomogeneous (IH) case, $U_d eq U_p$. For the H case at half filling, we found that the global magnetization rises sharply at weak coupling, and then stabilizes towards the strong-coupling (Heisenberg) value, as a result of the interplay between the ferromagnetism of like sites and the antiferromagnetism between unlike sites; we verified that the system is an insulator for all $U$. For the IH system at half filling, we argue that the case $U_p eq U_d$ falls under Liebs theorem, provided they are positive definite, so we used DQMC to probe the cases $U_p=0,U_d=U$ and $U_p=U, U_d=0$. We found that the different environments of $d$ and $p$ sites lead to a ferromagnetic insulator when $U_d=0$; by contrast, $U_p=0$ leads to to a metal without any magnetic ordering. In addition, we have also established that at density $rho=1/3$, strong antiferromagnetic correlations set in, caused by the presence of one fermion on each $d$ site.
One of the biggest puzzles concerning the cuprate high temperature superconductors is what determines the maximum transition temperature (Tc,max), which varies from less than 30 K to above 130 K in different compounds. Despite this dramatic variation, a robust trend is that within each family, the double-layer compound always has higher Tc,max than the single-layer counterpart. Here we use scanning tunneling microscopy to investigate the electronic structure of four cuprate parent compounds belonging to two different families. We find that within each family, the double layer compound has a much smaller charge transfer gap size ($Delta_{CT}$), indicating a clear anticorrelation between $Delta_{CT}$ and Tc,max. These results suggest that the charge transfer gap plays a key role in the superconducting physics of cuprates, which shed important new light on the high Tc mechanism from doped Mott insulator perspective.
We show that Liebs concavity theorem holds more generally for any unitarily invariant matrix function $phi:mathbf{H}^n_+rightarrow mathbb{R}$ that is monotone and concave. Concretely, we prove the joint concavity of the function $(A,B) mapstophibig[(B^frac{qs}{2}K^*A^{ps}KB^frac{qs}{2})^{frac{1}{s}}big] $ on $mathbf{H}_+^mtimesmathbf{H}_+^n$, for any $Kin mathbb{C}^{mtimes n},sin(0,1],p,qin[0,1], p+qleq 1$.
The heavy-electron superconductor CeCoIn$_5$ exhibits a puzzling precursor state above its superconducting critical temperature at $T_c$ = 2.3 K. The thermopower and Nernst signal are anomalous. Below 15 K, the entropy current of the electrons undergoes a steep decrease reaching $sim$0 at $T_c$. Concurrently, the off-diagonal thermoelectric current $alpha_{xy}$ is enhanced. The delicate sensitivity of the zero-entropy state to field implies phase coherence over large distances. The prominent anomalies in the thermoelectric current contrast with the relatively weak effects in the resistivity and magnetization.
Mappings between models may be obtained by unitary transformations with preservation of the spectra but in general a change in the states. Non- canonical transformations in general also change the statistics of the operators involved. In these cases one may expect a change of topological properties as a consequence of the mapping. Here we consider some dualities resulting from mappings, by systematically using a Majorana fermion representation of spin and fermionic problems. We focus on the change of topological invariants that results from unitary transformations taking as examples the mapping between a spin system and a topological superconductor, and between different fermionic systems.
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