Spin and charge dynamics of a quasi-one-dimensional antiferromagnetic metal

We use quantum Monte Carlo simulations to study a finite-temperature dimensional-crossover-driven evolution of spin and charge dynamics in an anisotropic two-dimensional system of weakly coupled Hubbard chains with a half-filled band. The low-temperature behavior of the charge gap indicates a crossover between two distinct energy scales: a high-energy one-dimensional (1D) Mott gap due to the umklapp process and a low-energy gap which stems from long-range antiferromagnetic (AF) spin fluctuations. Away from the 1D regime and at temperature scales above the charge gap, the emergence of a zero-frequency Drude-like feature in the interchain optical conductivity ${\sigma }_{\perp }\left(\omega \right)$ implies the onset of a higher-dimensional metal. In this metallic phase, enhanced quasiparticle scattering off finite-range AF spin fluctuations results in incoherent single-particle dynamics. The coupling between spin and charge fluctuations is also seen in the spin dynamical structure factor $S(q,\omega )$ displaying damped spin excitations (paramagnons) close to the AF wave vector $q=(\pi ,\pi )$ and particle-hole continua near 1D momentum transfers spanning quasiparticles at the Fermi surface. We relate our results to the charge deconfinement in quasi-1D organic Bechgaard-Fabre salts.

Figure 1

Uniform charge susceptibility $ln\left({\chi }_{c}t\right)$ vs $1/T$ for several values of the interchain hopping $t_{\perp }$ found on a $16\times 16$ lattice. The inset shows the evolution of the QP gap ${\Delta }_{qp}$ on increasing $t_{\perp }$ extracted from a linear fit.

Figure 2

Temperature dependence of the static spin structure factor $S\left(q\right)$ found on a $16\times 16$ lattice: (a) $q=(\pi ,0)$ and (b) $q=(\pi ,\pi )$. The inset shows the finite-size scaling of the staggered magnetic moment $m_s$ for $t_{\perp }/t=0.2$ at $T=t/10$, $t/20$, and $t/30$.

Figure 3

Metal-insulator crossover in weakly coupled 1D chains upon increasing interchain hopping $t_{\perp }$. The plot shows (a) intra- ${\sigma }_{\parallel }\left(\omega \right)$ and (b) interchain ${\sigma }_{\perp }\left(\omega \right)$ optical spectra found on a $16\times 16$ lattice at $T=t/20$. From bottom to top: $t_{\perp }/t=0.05$, 0.1, 0.15, 0.2, 0.25, and 0.3.

Figure 4

Metal-insulator crossover in weakly coupled 1D chains upon decreasing temperature $T$. The plot shows (a) intra- ${\sigma }_{\parallel }\left(\omega \right)$ and (b) interchain ${\sigma }_{\perp }\left(\omega \right)$ optical spectra at $t_{\perp }/t=0.2$ (solid) and $t_{\perp }/t=0.1$ (dashed). From top to bottom: $T=t/10$, $t/16$, $t/20$, and $t/30$. For $t_{\perp }/t=0.1$, a complete optical gap develops at $T=t/20$ and we expect at lower temperatures qualitatively similar spectra (not shown).

Figure 5

Single-particle spectral function $A(k,\omega )$ obtained at $T=t/20$ on (a) 32-site chain with a dummy transverse momentum and (b), (c) $16\times 16$ lattice with $t_{\perp }/t=0.15$ (middle) and $t_{\perp }/t=0.3$ (bottom). Solid line in panel (c) gives the paramagnetic Hartee-Fock band structure.

Figure 6

The noninteracting Fermi surface with $t_{\perp }/t=0.3$ (solid) and of the purely 1D case (dashed).

Figure 7

Dimensional-crossover-driven evolution of the real part of the Green's function for fixed $T=t/20$ at the nodal $k=(\pi /2,\pi /2)$ point. Insets show the corresponding (left) low-frequency dependence of the imaginary part of the self-energy and (right) single-particle spectral function from bottom to top: $t_{\perp }/t=0.05$, 0.1, 0.15, 0.2, 0.25, and 0.3.

Figure 8

Same as in Fig. 7 but at the antinodal $k=(\pi /2,0)$ point.

Figure 9

(a) Dynamical charge structure factor $C(q,\omega )$ and (b) dynamical spin structure factor $S(q,\omega )$ obtained on a 32-site chain at $T=t/20$. The transverse momentum is a dummy label.

Figure 10

(a) Dynamical charge structure factor $C(q,\omega )$, and (b) dynamical spin structure factor $S(q,\omega )$ obtained on a $16\times 16$ lattice with $t_{\perp }/t=0.15$ at $T=t/20$. Solid line in panel (b) gives the LSWT dispersion Eq. (19) with $J_{\perp }/J=0.06$ and $J^{\prime }/J_{\perp }=0.2$. The chosen exchange couplings are fit parameters subject to the constraint of a finite magnetic order parameter in LSWT consistent with the long-range AF order in the system.

Figure 11

Same as in Fig. 10 but for $t_{\perp }/t=0.3$.

Figure 12

Temperature dependence of the dynamical spin structure factor $S(q,\omega )$ obtained on a $16\times 16$ lattice with fixed $t_{\perp }/t=0.2$: (a) $T=t/10$, (b) $T=t/20$, and (c) $T=t/30$. Insets show the single-particle spectral function at $k=(\pi /2,\pi /2)$ (left) and low-frequency dependence of the imaginary part of the corresponding self-energy (right).

Figure 13

Temperature dependence of the dynamical charge structure factor $C(q,\omega )$ obtained on a $16\times 16$ lattice with fixed $t_{\perp }/t=0.2$: (a) $T=t/10$, (b) $T=t/20$, and (c) $T=t/30$.