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Chapter 4 Electron Transport Near the 2D Mott Transition
Published in Sergey Kravchenko, Strongly Correlated Electrons in Two Dimensions, 2017
Tetsuya Furukawa, Kazushi Kanoda
Classical phase transition and concomitant critical phenomenon around a critical point between high-and low-temperature phases is driven by thermal fluctuations, where the former phase has larger entropy than the latter In contrast, quantum phase transition and accompanied quantum criticality are driven by quantum fluctuations between two competing ground states (Sachdev, 2011; Sondhi et al., 1997). For the case of the quantum-critical phenomena of the Mott transition, competing energies are on-site Coulomb repulsion energy U and bandwidth W. Quantum-critical fluctuations due to the competition can be enhanced at temperatures well below these energy scales. Hence, even if the critical temperature of the Mott transition, Tc, is finite, unlike the genuine quantum phase transition, in which Tc = 0K, in case Tc is orders of magnitude lower than W and U, there is a wide temperature region of Tc<T≪U, $ T_{c} < T{ \ll }U, $ W, where the system is subjected to quantum fluctuations (Fig. 4.3) and exhibits a quantum criticality of the Mott transition without the effect of thermal critical fluctuations around the finite-temperature critical point.
Preservation and enhancement of quantum correlations under Stark effect
Published in Journal of Modern Optics, 2023
Nitish Kumar Chandra, Rajiuddin Sk, Prasanta K. Panigrahi
Recently, Girolami et al. [14] proposed a computable discord type measure based on local quantum uncertainty (LQU). It uses skew information and fulfils all the conditions to be a physical quantum correlation measure [15]. The calculation of this measure avoids the difficult step of optimization and fulfils contractivity, which is not adequately proven by geometric discord based on the Hilbert-Schmidt norm [16]. In particular, LQU plays a significant role in determining the critical points of quantum phase transitions in multipartite spin systems better than quantum discord and exhibits correlations that are not captured by quantum entanglement, or quantum discord [17]. LQU is also associated with quantum Fisher information, which is known to play an essential role in quantum parameter estimation [18].
Quantum correlations in anisotropic XY-spin chains in a transverse magnetic field
Published in Phase Transitions, 2018
F. Mofidnakhaei, F. Khastehdel Fumani, S. Mahdavifar, J. Vahedi
In quantum many-body systems, a sudden change in the ground states at zero temperature is called quantum phase transition (QPT), which is driven by a variation of a coupling and/or an external parameter [1]. While all finite temperature transitions, called classical phase transitions, are driven by thermal fluctuations, the main characteristic of QPTs is due to the Heisenberg uncertainty relation. The discontinuities in the ground state energy are related to the energy level crossings, which determine the QPTs order. Depending on a discontinuity in the ground state energy or in the first derivative of the ground state energy, QPTs are characterized as first-order transition or second-order phase transition, respectively.
Effect of neighbouring molecules on ground-state properties of many-body polar linear rotor systems
Published in Molecular Physics, 2023
Tapas Sahoo, Gautam Gangopadhyay
When solving the time-dependent or independent Schrödinger equation for a non-ideal system, it is often convenient to construct the wavefunction as a product of known basis functions. If there are D degrees of freedom (DOFs) and each one requires n basis functions, the size of the array required to store the wave function will be , and for the Hamiltonian matrix, . Consequently, the computational cost of the exact basis set methods increases exponentially with the number of DOFs. This significantly oversized memory makes the exact methods impractical. However, the Density Matrix Renormalization Group (DMRG) [4–7] method is most effective for a many-body quantum problem when the system is of low dimension (in general) and the interaction energy is pair-wise additive. Recently, theoretical investigations of such confined systems of up to 100 linear rotors have been carried out employing the DMRG [8] and Multi-Layer Multi-Configuration Time-Dependent Hartree [9] methods. In addition, the DMRG approach [10–14] has been extended for the confined asymmetric top rotors pinned to a one-dimensional chain. The quantum phase transition was witnessed in both studies as entanglement entropy. However, DMRG will not be the automatic choice if the interaction between the molecules is not considered to be a pairwise additive. An alternative approach for the simulation of many-body non-ideal systems is the Path integral Monte Carlo methodology [15], which is capable of simulating systems with any form of interaction. The arbitrary size of the system can be simulated. Indeed, the Path Integral approaches are suitable for studying quantum many-body systems, since the computational cost of this Monte Carlo-based method [16] is low compared to the other methods.