Dissipation-Driven Transition of Particles from Dispersive to Flat Bands

Abstract

Flat bands (FBs) play a crucial role in condensed matter physics, offering an ideal platform to study strong correlation effects and enabling applications in diffraction-free photonics and quantum devices. However, the study and application of FB properties are susceptible to interference from dispersive bands. Here, we explore the impact of bond dissipation on systems hosting both flat and dispersive bands by calculating the steady-state density matrix. We demonstrate that bond dissipation can drive particles from dispersive bands into FBs and establish the general conditions for this phenomenon to occur. Our results demonstrate that dissipation can facilitate FB preparation, property measurement, and utilization. This opens a new avenue for exploring FB physics in open quantum systems, with potential implications for strongly correlated physics.

Figures (12)

• Figure 1: Lattice structures and CLS configurations for the (a) cross-stitch ($U=1$) and (c) sawtooth ($U=2$) models. Filled circles denote sites occupied by the CLS. The corresponding energy spectra are shown in (b) and (d), respectively. For the cross-stitch model, the inter-cell and intra-cell hoppings are set to $-1$ and $0$, respectively. For the sawtooth model, the intra-cell hopping is $-\sqrt{2}$, with inter-cell hoppings of $-\sqrt{2}$ between upper and lower chains, and $-1$ between sites on the lower chain. Throughout this work, onsite energies are set to $0$, and open boundary conditions are used.
• Figure 2: Steady-state density matrix $\rho_{ss}$ of the cross-stitch model under bond dissipation with $q=1$ and $O_{j}^{u}=O_{j}^{l}$. (a, c): Matrix elements $|\rho_{mn}|$ in the eigenbasis of $H$ for $a=1$ and $a=-1$, respectively. Dashed lines separate the FB region in the center from the dispersive bands on the sides. (b, d): Eigenvalue spectra of $\rho_{ss}$ for $a=1$ and $a=-1$, respectively, each showing a single nonzero value, confirming a pure steady state. Insets: real-space wavefunctions corresponding to the nonzero eigenvalue. Here, we consider $20$ unit cells and set $\Gamma=1$ on both chains.
• Figure 3: Steady-state density matrix $\rho_{ss}$ of the sawtooth model under bond dissipation with $q=2$ and $O_{j}^{u}=O_{j}^{l}$. Matrix elements $|\rho_{mn}|$ in the eigenbasis of $H$ for (a) $a=1$ and (b) $a=-1$, respectively. Dashed lines mark the boundary between the FB and dispersive bands. Eigenvalue spectra of $\rho_{ss}$ for (c) $a=1$ and (d) $a=-1$, both featuring a single nonzero eigenvalue. The real-space distribution of the corresponding eigenstate is shown in the insets. Here, we fix $L=20$.
• Figure 4: (a) Twisted-bilayer square lattice with rotation angle $\theta$. Red (blue) dots represent sites in layer $1$ ($2$), and black dots indicate superlattice sites where the two layers align vertically. (b) Single-particle spectrum at $\theta = 36.87^\circ$ for $t_{\perp} = 10$, $\Delta = 10$, and $l_0 = 0.15$. Bond dissipation is applied between neighboring black sites on layer $1$ only. The results are the same along the directions indicated by green and yellow lines. (c) Steady-state density matrix $|\rho_{mn}|$ in the eigenbasis of $H$ for $a=-1$. The diagonal elements are shown in (d). The dashed lines separate the nearly FB region from the dispersive band region. Here, we consider each layer to consist of a $7 \times 7$ lattice.
• Figure 5: (a1, b1, c1) Many-body energy spectra for interaction strengths $V=0.5$, $1$, and $2$, respectively. (a2, b2, c2) Corresponding steady-state density matrix elements $|\rho_{mn}|$ in the eigenbasis of the many-body Hamiltonian. (d) Occupation $P$ as a function of interaction strength $V$. Here, we fix the number of unit cells to $N=6$, the particle number to $2$, and set $t_0=10$, $t_1=1$.