Zihan Cheng
@utexas.edu
The University of Texas at Austin
Scopus Publications
Scholar Citations
Scholar h-index
Scholar i10-index
Scopus Publications
Jianxiong Zhai, Zihan Cheng, Yu Zhang, and Youqi Ke
American Physical Society (APS)
Eli Chertkov, Zihan Cheng, Andrew C. Potter, Sarang Gopalakrishnan, Thomas M. Gatterman, Justin A. Gerber, Kevin Gilmore, Dan Gresh, Alex Hall, Aaron Hankin,et al.
Springer Science and Business Media LLC
Zihan Cheng and Matteo Ippoliti
American Physical Society (APS)
We introduce a classical algorithm for sampling the output of shallow, noisy random circuits on two-dimensional qubit arrays. The algorithm builds on the recently-proposed"space-evolving block decimation"(SEBD) and extends it to the case of noisy circuits. SEBD is based on a mapping of 2D unitary circuits to 1D {\\it monitored} ones, which feature measurements alongside unitary gates; it exploits the presence of a measurement-induced entanglement phase transition to achieve efficient (approximate) sampling below a finite critical depth $T_c$. Our noisy-SEBD algorithm unravels the action of noise into measurements, further lowering entanglement and enabling efficient classical sampling up to larger circuit depths. We analyze a class of physically-relevant noise models (unital qubit channels) within a two-replica statistical mechanics treatment, finding weak measurements to be the optimal (i.e. most disentangling) unraveling. We then locate the noisy-SEBD complexity transition as a function of circuit depth and noise strength in realistic circuit models. As an illustrative example, we show that circuits on heavy-hexagon qubit arrays with noise rates of $\\approx 2\\%$ per CNOT, based on IBM Quantum processors, can be efficiently sampled up to a depth of 5 iSWAP (or 10 CNOT) gate layers. Our results help sharpen the requirements for practical hardness of simulation of noisy hardware.
Zihan Cheng and Andrew C. Potter
American Physical Society (APS)
We present a numerical method to simulate non-equilibrium Floquet steady states of one-dimensional periodically-driven (Floquet) many-body systems coupled to a dissipative bath, called open-system Floquet DMRG (OFDMRG). This method is based on a matrix product operator ansatz for the Floquet density matrix in frequency-space, and enables access to large systems beyond the reach of exact master-equation or quantum trajectory simulations, while retaining information about the periodic micro-motion in Floquet steady states. An excited-state extension of this technique also allows computation of the dynamical approach to the steady state on asymptotically long timescales. We benchmark the OFDMRG approach with a driven-dissipative Ising model, and apply it to study the possibility of dissipatively stabilizing pre-thermal discrete time-crystalline order by coupling to a cold bath.
Jianxiong Zhai, Rui Xue, Zihan Cheng, and Youqi Ke
American Physical Society (APS)
The auxiliary and itinerant coherent potential approximations (ACPA and ICPA) have been proposed as effective methods for treating both mass and force-constant disorder in lattice vibration. In this work we make a direct comparison of ACPA and ICPA to identify the differences between these two methods for simulating vibrational properties of disordered materials and devices. We investigate the major approximations in the disorder self-energies of these two methods by using the diagrammatic method. The single-site ACPA neglects the crossing diagrams describing nonlocal correlations, while ICPA utilizes only the single-fluctuation states in the self-consistency and presents extra errors due to a change in the terms with nearest-neighbor fluctuation. To further demonstrate the important differences between the ACPA and ICPA in the phonon spectral and transport properties, we extend ICPA in combination with the Keldysh nonequilibrium Green's function technique to simulate quantum transport and introduce a Green's-function-based spectral unfolding technique to use with molecular ACPA and the supercell methods for comparison. By studying the disordered one- and three-dimensional alloys, we find that ACPA and ICPA agree very well in the weak scattering regime due to weak force-constant disorder or low phonon frequency. However, for the strong scattering of force-constant disorder, it is found that the two methods present important deviations in the linewidth (and height) of disorder-averaged phonon spectra. Compared to the ACPA and exact results, the problematic treatment of the nearest-neighbor fluctuation in ICPA can present unphysical scattering and induce large errors in the phonon transport, presenting important limitations of ICPA for transport simulation.
Ajesh Kumar, Zihan Cheng, and Andrew C. Potter
American Physical Society (APS)
We theoretically explore 2d moire heterostructures in lattice-commensurate magnetic fields as platforms for quantum simulation of a paradigmatic model of non-Fermi liquid physics: a Fermi-surface coupled to a fluctuating gauge field. In these moire-Hofstadter (MH) systems, long-wavelength acoustic phonons exhibit singular interactions with electrons analogous to those of electrons with 2d gauge fields. This leads to a breakdown of Fermi-liquid theory at low temperatures. We show that a combination of large moire-unit cell size, tunable Fermi-surface topology, and enhanced coupling to interlayer sliding modes, enhance these effects by over many orders-of-magnitude compared to bulk crystals, placing them within experimental reach. Though we find that the asymptotic low-temperature non-Fermi liquid regime remains at prohibitively low temperatures, striking precursor non-Fermi liquid signatures can be observed, and we propose surface acoustic wave attenuation and quantum oscillation transport experiments. We also study the motion of MH acoustic-polarons, which we predict exhibit logarithmically diverging effective mass and unconventional magnetic field scaling for scaling of cyclotron resonance frequency and quantum oscillation amplitude.
Zihan Cheng, Mankun Sang, Jianxiong Zhai, and Youqi Ke
American Physical Society (APS)
We report the auxiliary coherent potential approximation (ACPA) for calculating the phonon dispersion of three-dimensional alloys with both mass and force-constant disorders. To obtain the average spectra function of disordered alloys, the average coherent scattering structure factors are derived from the auxiliary coherent medium in single-site approximation. We provide an analytical proof of the sum rule in the auxiliary coherent medium, which ensures the analyticity of physical properties. To demonstrate the accuracy and applicability of the ACPA method, we apply the ACPA to calculate phonon dispersion of several alloys, including CuPd CuAu, PdFe, and NiPt with different disorder concentrations. We find the ACPA phonon dispersion results agree very well with the itinerant coherent potential approximation calculations and experimental measurements. The approximate separable force-constant model used in the ACPA can very well represent the first-principles disordered force constants, presenting minor or even negligible influence on the phonon dispersion of the alloy. The ACPA model features easy implementation and high computational efficiency, providing an effective method for simulating vibrational properties of realistic alloys.
Jianxiong Zhai, Qingyun Zhang, Zihan Cheng, Jie Ren, Youqi Ke, and Baowen Li
American Physical Society (APS)
Wave transport through disordered materials is of broad interest in science and engineering. It has been generally believed that long-range transport cannot exist in low-dimensional disordered systems due to the Anderson localization of all states. However, in this work we report the anomalous transparency of phonon transport induced by cooperative effects of mass and force-constant disorders in completely random harmonic wires. In contrast to the full localization in mass-disordered wire, an anomalous transparent phonon state can emerge due to the intrinsic cooperation of disordered mass and force constants. We obtain the frequency of the transparent state, tuned by the disordered force constants and masses. Consequently, the phonon transport in the completely disordered system falls into three different regimes: the full localization, resonant, and sub-ballistic regimes. While there exists a single nonzero transparent frequency in the resonant regime, transparent states in a wide range of frequencies can be present in the sub-ballistic regime, which significantly enhances the thermal conductivity of disordered wires. These findings may open new doors to modulate thermal transport and design thermal devices, including thermal filter and high-thermal-conductivity materials.
Zihan Cheng, Jianxiong Zhai, Qingyun Zhang, and Youqi Ke
American Physical Society (APS)
The inevitable and random impurities or defects can significantly influence the lattice-vibrational properties of materials and devices. Thus, the capability of effectively treating disorder effects is indispensable for theoretical simulations. In this paper, we report an auxiliary coherent medium theory, in the framework of multiple scattering theory, to simulate disordered vibrational systems containing both mass and force-constant disorders. In this method, the physical Green's function is related to an auxiliary Green's function by introducing a separable force-constant model to describe disordered systems. As an important result, the force-constant disorder can be transformed to a diagonal-like disorder in the auxiliary Hamiltonian while maintaining the important force-constant sum rule. In combination with the single-site and cluster coherent potential approximation, the configurational average over the auxiliary Green's function can be performed to obtain the configuration-averaged physical properties. To demonstrate the effectiveness of this method, we apply it to a one-dimensional harmonic chain with atomic disorders and find our calculations agree very well with the exact results for a wide range of mass and force constants. Moreover, we show that the phonon transport property of disordered devices can be derived based on the auxiliary Green's function formalism in combination with vertex corrections. The auxiliary coherent medium theory features easy implementation and feasible incorporation with diagrammatic technique in many-body perturbation and various cluster approximations, providing an important approach to analyze disorder effects on the vibrational properties. Moreover, it is also straightforward to apply the present formalism to treat the general atomic disorder in electronic systems.