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Register a new userOn quantum quenches at one loop
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We study global quenches in a number of interacting quantum field theory models away from the conformal regime. We conduct a perturbative renormalization at one-loop level and track the modifications of the quench protocol induced by the renormalization group flow. The scaling of various observables at early times is evaluated in the regime of rapid quench rates, with a particular emphasis placed on the leading order effects that cannot be recovered using the finite order conformal perturbation theory. We employ the canonical ideas of effective action to verify our results and discuss a potential route towards understanding the late time dynamics.
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A tensorial representation of $phi^4$ field theory introduced in Phys. Rev. D. 93, 085005 (2016) is studied close to six dimensions, with an eye towards a possible realization of an interacting conformal field theory in five dimensions. We employ the two-loop $epsilon$-expansion, two-loop fixed-dimension renormalization group, and non-perturbative functional renormalization group. An interacting, real, infrared-stable fixed point is found near six dimensions, and the corresponding anomalous dimensions are computed to the second order in small parameter $epsilon=6-d$. Two-loop epsilon-expansion indicates, however, that the second-order corrections may destabilize the fixed point at some critical $epsilon_c <1$. A more detailed analysis within all three computational schemes suggests that the interacting, infrared-stable fixed point found previously collides with another fixed point and becomes complex when the dimension is lowered from six towards five. Such a result would conform to the expectation of triviality of $O(2)$ field theories above four dimensions.
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We investigate the Joule expansion of nonintegrable quantum systems that contain bosons or spinless fermions in one-dimensional lattices. A barrier initially confines the particles to be in half of the system in a thermal state described by the canonical ensemble and is removed at time $t = 0$. We investigate the properties of the time-evolved density matrix, the diagonal ensemble density matrix and the corresponding canonical ensemble density matrix with an effective temperature determined by the total energy conservation using exact diagonalization. The weights for the diagonal ensemble and the canonical ensemble match well for high initial temperatures that correspond to negative effective final temperatures after the expansion. At long times after the barrier is removed, the time-evolved Renyi entropy of subsystems bigger than half can equilibrate to the thermal entropy with exponentially small fluctuations. The time-evolved reduced density matrix at long times can be approximated by a thermal density matrix for small subsystems. Few-body observables, like the momentum distribution function, can be approximated by a thermal expectation of the canonical ensemble with strongly suppressed fluctuations. The negative effective temperatures for finite systems go to nonnegative temperatures in the thermodynamic limit for bosons, but is a true thermodynamic effect for fermions, which is confirmed by finite temperature density matrix renormalization group calculations. We propose the Joule expansion as a way to dynamically create negative temperature states for fermion systems with repulsive interactions.
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