The antiferromagnetic $J_1-J_2$ model is a spin-1/2 chain with isotropic exchange $J_1 > 0$ between first neighbors and $J_2 = αJ_1$ between second neighbors. The model supports both gapless quantum phases with nondegenerate ground states and gapped phases with $Δ(α) > 0$ and doubly degenerate ground states. Exact thermodynamics is limited to $α= 0$, the linear Heisenberg antiferromagnet (HAF). Exact diagonalization of small systems at frustration $α$ followed by density matrix renormalization group (DMRG) calculations returns the entropy density $S(T,α,N)$ and magnetic susceptibility $χ(T,α,N)$ of progressively larger systems up to $N = 96$ or 152 spins. Convergence to the thermodynamics limit, $S(T,α)$ or $χ(T,α)$, is demonstrated down to $T/J \sim 0.01$ in the sectors $α< 1$ and $α> 1$. $S(T,α)$ yields the critical points between gapless phases with $S^\prime(0,α) > 0$ and gapped phases with $S^\prime(0,α) = 0$. The $S^\prime(T,α)$ maximum at $T^*(α)$ is obtained directly in chains with large $Δ(α)$ and by extrapolation for small gaps. A phenomenological approximation for $S(T,α)$ down to $T = 0$ indicates power-law deviations $T^{-γ(α)}$ from $\exp(-Δ(α)/T)$ with exponent $γ(α)$ that increases with $α$. The $χ(T,α)$ analysis also yields power-law deviations, but with exponent $η(α)$ that decreases with $α$. $S(T,α)$ and the spin density $ρ(T,α) = 4Tχ(T,α)$ probe the thermal and magnetic fluctuations, respectively, of strongly correlated spin states. Gapless chains have constant $S(T,α)/ρ(T,α)$ for $T < 0.10$. Remarkably, the ratio decreases (increases) with $T$ in chains with large (small) $Δ(α)$.
Magnetic field effects on two-leg Heisenberg antiferromagnetic ladders: Thermodynamic properties
利用最近发展起来的转移矩阵重整化群方法，研究了磁场中两条腿反铁磁梯的热力学性质。基于不同的磁化行为，我们发现了无序自旋液体，Luttinger液体，自旋极化相和依赖于磁场和温度的经典制度。我们在Luttinger液相区的计算表明，在Cu $_2$（C $_5$ H $_{12}$ N $_2$）$_2$ Cl $_4$ }上观察到的NMR弛豫速率发散和反常比热行为都是由于准一维效应而不是三维有序.
Entropy and electronic orders of the three-orbital Hubbard model with antiferromagnetic Hund coupling
多轨道Hubbard系统中的反铁磁Hund耦合导致轨道冻结和相关的超导不稳定性，以及在奇数轨道的情况下的独特的复合订单。虽然半满三轨道模型的富相图最近已被详细探讨，掺杂系统的性质仍有待澄清。在这里，我们通过计算半填充模型的熵来补充以前的研究，该模型表现出轨道冻结区域的增加和复合有序相的抑制。掺杂相关相图表明，复合有序态可以稳定在掺杂的莫特制度，如果传统的电子秩序被抑制的挫折。虽然反铁轨道序占主导地位的填充范围$2\lesssim n \le 3$，和铁轨道序的强相互作用区域的$1\lesssim n < 2$，我们发现一个非常高的$T_c$周围$n=1.5$（四分之一填充）的超导性。在掺杂体系中，轨道冻结交叉与超导电性之间也存在着密切的联系。
Numerical study of non-adiabatic quantum thermodynamics of the driven resonant level model: Non-equilibrium entropy production and higher order corrections
本文对非平衡条件下的共振能级模型的量子热力学进行了数值研究。在我们之前关于非平衡量子热力学的工作（Phys. Rev. B 101，184304 [2020]）之后，我们将密度算符扩展为驱动速度的幂级数，在那里我们可以确定非绝热热力学量。特别地，我们计算了非平衡熵产生率以及对能量和/或布居的高阶非绝热修正。在弱耦合的限制下，我们的结果退化为量子主方程的结果。
