We develop a biorthogonal time-dependent variational principle for real-time dynamics of non-Hermitian quantum many-body systems. Independent left and right matrix-product states obey coupled bivariational tangent-space equations whose cross-Gram matrix defines an oblique projection. A matrix-free scaled Taylor action propagates the resulting non-normal local generators without assembling dense matrices or storing a Krylov basis. We distinguish the fully coupled algorithm, which solves the cross-pairing problem and truncates the two bond bases jointly, from an efficient independently propagated approximation used for large systems. Independent truncation can make the retained left-right pairing nearly singular; overlap drift and the smallest singular value of the bond cross matrix expose this failure, while coupled truncation substantially delays it. Exact benchmarks and convergence tests validate the method. Applied to an interacting long-range non-Hermitian Ising chain, it resolves a biorthogonal dynamical quantum phase transition and shows that a weak imaginary field shifts the leading critical time from $t^{\ast}|J|=1.84$ to $1.04$.
Global quenches at one-dimensional critical points admit a boundary conformal field theory (BCFT) description in which Euclidean strip correlators are analytically continued to real time. We formulate this construction for interacting non-Hermitian critical systems, where a right ket alone does not specify the dynamica...
Computing multiple eigenstates of non-Hermitian many-body operators plays an important role in investigating excitation spectra, spectral properties, and relaxation dynamics in interacting and open quantum systems. However, this task is challenging because the eigenvectors are generally nonorthogonal and the Hilbert sp...
Xing-Yao Wu, Zhang Yang, Yan-Bin Chen et al.· 0 citations
We study the roles of broken spectra and exceptional points in finite-time driven non-Hermitian fermionic dynamics. We compute the Nambu biorthogonal correlation matrix for this purpose. The imbalanced-pairing Kitaev chain serves as our concrete realization. Transient passage through a broken-spectrum region amplifies...
Universal scaling generated when a strongly interacting quantum many-body system is driven across a continuous phase transition provides a dynamical probe of equilibrium criticality. Accessing this regime numerically in two dimensions is challenging because it requires accurate real-time evolution of correlated many-bo...
Linda Mauron, Luciano Loris Viteritti, Z. Denis et al.· 0 citations
This work presents a time-dependent (TD) unitary coupled-cluster (UCC) formulation for electronic quantum dynamics, including the propagation of excited states and their superpositions, in both single- and multi-reference regimes. Standard TD coupled-cluster techniques offer size-extensivity, but they rely on non-Hermi...
Schrödingerization maps a non-unitary linear evolution to a unitary dynamics on an enlarged Hilbert space. For ill-posed equations, such as backward diffusion, this does not remove the instability of the recovered physical variable, but it makes the phase-space language of quantum propagation available. We show that th...
