Xi Chen ^a , Shi-Ju Ran ^b,c , Tao Liu ^d , Cheng Peng ^e , Yi-Zhen Huang ^e , Gang Su ^a,f,⇑

^a School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

^b Department of Physics, Capital Normal University, Beijing 100048, China

^c ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain

^d School of Science, Hunan University of Technology, Zhuzhou 412007, China

^e School of Physics and Astronomy, Shanghai Jiaotong University, Shanghai 200240, China

^f Kavli Institute for Theoretical Sciences, and CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China

Quantum fluctuations from frustration can trigger quantum spin liquids (QSLs) at zero temperature. However, it is unclear how thermal fluctuations affect a QSL. We employ state-of-the-art tensor network-based methods to explore the ground state and thermodynamic properties of the spin-1=2 kagomé Heisenberg antiferromagnet (KHA). Its ground state is shown to be consistent with a gapless QSL by observing the absence of zero-magnetization plateau as well as the algebraic behaviors of susceptibility and specific heat at low temperatures, respectively. We show that there exists an algebraic paramagnetic liquid (APL) that possesses both the paramagnetic properties and the algebraic behaviors inherited from the QSL. The APL is induced under the interplay between quantum fluctuations from geometrical frustration and thermal fluctuations. By studying the temperature-dependent behaviors of specific heat and magnetic susceptibility, a finite-temperature phase diagram in a magnetic field is suggested, where various phases are identified. This present study gains useful insight into the thermodynamic properties of the spin-1/2 KHA with or without a magnetic field and is helpful for relevant experimental studies.