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Register a new userDefect production in non-linear quench across a quantum critical point
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Added by
Krishnendu Sengupta
Publication date
2008
fields
Physics
and research's language is
English
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We show that the defect density $n$, for a slow non-linear power-law quench with a rate $tau^{-1}$ and an exponent $alpha>0$, which takes the system through a critical point characterized by correlation length and dynamical critical exponents $ u$ and $z$, scales as $n sim tau^{-alpha u d/ (alpha z u+1)}$ [$n sim (alpha g^{(alpha-1)/alpha}/tau)^{ u d/(z u+1)}$], if the quench takes the system across the critical point at time $t=0$ [$t=t_0 e 0$], where $g$ is a non-universal constant and $d$ is the system dimension. These scaling laws constitute the first theoretical results for defect production in non-linear quenches across quantum critical points and reproduce their well-known counterpart for linear quench ($alpha=1$) as a special case. We supplement our results with numerical studies of well-known models and suggest experiments to test our theory.
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We study defect production in a quantum system subjected to a nonlinear power law quench which takes it either through a quantum critical or multicritical point or along a quantum critical line. We elaborate on our earlier work [D. Sen, K. Sengupta, S. Mondal, prl 101, 016806 (2008)] and present a detailed analysis of the scaling of the defect density $n$ with the quench rate $tau$ and exponent $al$ for each of the above-mentioned cases. We also compute the correlation functions for defects generated in nonlinear quenches through a quantum critical point and discuss the dependence of the amplitudes of such correlation functions on the exponent $al$. We discuss several experimental systems where these theoretical predictions can be tested.
We compute the transition temperature $T_c$ and the Ginzburg temperature $T_{rm G}$ above $T_c$ near a quantum critical point at the boundary of an ordered phase with a broken discrete symmetry in a two-dimensional metallic electron system. Our calculation is based on a renormalization group analysis of the Hertz action with a scalar order parameter. We provide analytic expressions for $T_c$ and $T_{rm G}$ as a function of the non-thermal control parameter for the quantum phase transition, including logarithmic corrections. The Ginzburg regime between $T_c$ and $T_{rm G}$ occupies a sizable part of the phase diagram.
At the familiar liquid-gas phase transition in water, the density jumps discontinuously at atmospheric pressure, but the line of these first-order transitions defined by increasing pressures terminates at the critical point, a concept ubiquitous in statistical thermodynamics. In correlated quantum materials, a critical point was predicted and measured terminating the line of Mott metal-insulator transitions, which are also first-order with a discontinuous charge density. In quantum spin systems, continuous quantum phase transitions (QPTs) have been investigated extensively, but discontinuous QPTs have received less attention. The frustrated quantum antiferromagnet SrCu$_2$(BO$_3$)$_2$ constitutes a near-exact realization of the paradigmatic Shastry-Sutherland model and displays exotic phenomena including magnetization plateaux, anomalous thermodynamics and discontinuous QPTs. We demonstrate by high-precision specific-heat measurements under pressure and applied magnetic field that, like water, the pressure-temperature phase diagram of SrCu$_2$(BO$_3$)$_2$ has an Ising critical point terminating a first-order transition line, which separates phases with different densities of magnetic particles (triplets). We achieve a quantitative explanation of our data by detailed numerical calculations using newly-developed finite-temperature tensor-network methods. These results open a new dimension in understanding the thermodynamics of quantum magnetic materials, where the anisotropic spin interactions producing topological properties for spintronic applications drive an increasing focus on first-order QPTs.
A quantum critical point (QCP) of the heavy fermion Ce(Ru_{1-x}Rh_x)_2Si_2 (x = 0, 0.03) has been studied by single-crystalline neutron scattering. By accurately measuring the dynamical susceptibility at the antiferromagnetic wave vector k_3 = 0.35 c^*, we have shown that the energy width Gamma(k_3), i.e., inverse correlation time, depends on temperature as Gamma(k_3) = c_1 + c_2 T^{3/2 +- 0.1}, where c_1 and c_2 are x dependent constants, in a low temperature range. This critical exponent 3/2 +- 0.1 proves that the QCP is controlled by that of the itinerant antiferromagnet.
We show that a closed quantum system driven through a quantum critical point with two rates $omega_1$ (which controls its proximity to the quantum critical point) and $omega_2$ (which controls the dispersion of the low-energy quasiparticles at the critical point) exhibits novel scaling laws for defect density $n$ and residual energy $Q$. We demonstrate suppression of both $n$ and $Q$ with increasing $omega_2$ leading to an alternate route to achieving near-adiabaticity in a finite time for a quantum system during its passage through a critical point. We provide an exact solution for such dynamics with linear drive protocols applied to a class of integrable models, supplement this solution with scaling arguments applicable to generic many-body Hamiltonians, and discuss specific models and experimental systems where our theory may be tested.
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